The most commonly accepted definition of Vaishnavas is people who believe Lord Vishnu to be supreme. But can a person call himself a Vaishnava while believing in Hari-Hara-abheda? What do different Vaishnava Sampradayas say regarding this?
Yes, a true Vaishnava do not differentiate between Lord Vishnu, Lord Shiva and Lord Brahma. It has been described by Lord Vishnu himself to Lord Brahma in Padma Purana, Part 10, Section 7 (KRIYAYOGASARAKHANDA), Chapter 2.
Those who look upon you, me and Sankara as equal, and who honour a guest, should be known to be Visnu's devotees.
Those who are free from devotion to heretics, who are highly devoted to Siva, who are engaged in (observing) the vow of Caturdasi, should be known to be Vais- navas.
In Vishnu Purana 5.33.47-49, it was said by Lord Krishna that only deluded person see difference in Me and Lord Shiva.
त्वया यदभयं दत्तं तद्दत्तमग्विलं मया ।
मत्तो विभिन्नमात्मानं द्रष्ट्रं नार्हसि शंकर ।।
योऽहं स त्वं जगच्चेदं स देवासुरमानुषम् ।
अविद्यामोहितात्मानः पुरुषा भिन्नदर्शिन ।।
That Abhaya which was given by you was also given by me. Oh Shankara do not see yourself different from me. That which is me the same is you, this entire creation, Devas, Manyushyas and Asuras. Only those who are deluded by Avidya see me and you as different.
The Harivaṃśa has a stotra extolling both the similarity and unified form of Viṣṇu and Śiva. There are even several epithets dedicated to them: Hariharātmaka and Agniṣomātmaka.The following is an excerpt from a stotra from the Harivaṃśa (Viṣṇu-parva) extolling both Viṣṇu and Śiva as identical and Supreme Lords:
Chapter 125 - Battle between Śrī Kṛṣṇa and lord Śiva
125.29 “Mārkaṇḍeya said—I offer my salutation to Śiva in the form of Viṣṇu, and Viṣṇu in the form of Śiva. I find no difference between the two. Observing my feelings, let both of them bestow welfare on me.”
... (more praise and comparing)
125.39 “The one who recites this stotra daily and the one who listen to it, he achieves te final beautitude by the grace of Viṣṇu and Rudra.”
125.40 “I shall offer prayer to Hari and Hara who are meeting Brahmā. Both of them are the supreme lords, besides being the creator and the destroyer of the world.”
125.41 “Lord Viṣṇu cannot exist without Śiva, and Śiva cannot exist without Viṣṇu. Therefore, in the earlier times, both of them had unified personality.”
125.42 “I offer my salutation to lord Rudra and Viṣṇu, who roam about in the world individually or collectively.”
The Harivaṃśa (escpecially the Viṣṇu-parva) has been quoted by many Gauḍiya-Vaiṣṇava Ācāryas (according to Bhumipati Dasa) and has been mentioned as an important Vaiṣṇava scripture by both Caitanya Mahāprabhu (in his Śrī Caitanya Caritāmṛta (source)) and by his disciple Sanātana Gosvāmī (in his auto-commentary Dig-darśinī on his Śrī Bṛhad-bhāgavatāmṛta (source))
The preceding context is interesting and in short relates that, Śiva, while protecting Bāṇāsura, was fighting a war with Śrī Kṛṣṇa. When Śiva was about to fire a weapon at Kṛṣṇa, Kṛṣṇa counter-attacked Śiva which overpowered him and he became over-exhausted.
After a while, the earth suffered greatly due to the effects of this battle and the earth-goddess (Dhāraṇī-devī) went to Brahmā for a solution:
125.14 “The Earth goddess said—O lord of gods, of valorous one, I am suffering from the great prowess. Having suffered considerably from the burden of lord Śiva, it appears that I shall have to submerge in the oceanic waters.”
Brahmā then meets with Śiva and utters his disapproval of the fighting, giving the first hint of his unity with Viṣṇu:
125.17: “I do not like your fighting with Śrī Kṛṣṇa - the valorous one. You are unable to understand Śrī Kṛṣṇa. In fact your own soul has been divided into two.”
After establishing this inseparable link (which no one was able to identify), Brahmā inquired the sage Mārkaṇḍeya for explaining the reason behind this aspect.
Mārkaṇḍeya’s answer is in the form of a stotra of which the above is an excerpt.
125.30 “The one who is the begining middle or end, who is indestructible and eternal being Akṣara—Brahma, his form is that of Hari-Hara of Brahman, I shall describe before you the same, Hari Harātmaka.”
125.35 “Rudra has also been known as the fire, while Viṣṇu has also been known as soma or the moon. Because of this, the entire universe, is also known as Agniṣomātmaka.”
A true Vaishnava is a devotee of Vishnu. He sees Vishnu in everything.
So for him Shiva is Vishnu only. So, the question does not even arise in the mind of a true Bhakta.
From the Kurma Purana:
Krishna’s worship to Maha Deva :
Shri Krishna had Eight Principal Wives viz. Rukmini, Satyabhama, Jambavati, Nagnajiti, Mitravinda, Lakshmana, Kalindi and Maadri, but accepted sixteen thousand maidens released from the prisons of Narakaasura whom he decimated. Rukmini had eight sons viz. Charudeshna, Suchaaru, Chaaruvesha, Yashodhara, Chaarushrava, Charuyasha, Pradyumna and Shankha. Similarly other wives had several sons. But Devi Jambavati longed to get an exemplary Son like Indra and on realising this wish decided to perform Parama Tapasya to Parama Shiva and left for the Ashram of Maharshi Upamanyu on the banks of Ganges.
Following the rules very strictly, Krishna followed the ‘Upadesha’ or the teachings and instructions of Upamanyu such as Paashupata Yoga, Paashupata Vrata and Paashupata Jnaana and incessantly recited Rudra Mantras with strict adherence of the formal and required form of worship to Mahadeva. After considerable effort, Shri Krishna visioned Maha Deva and Devi Parvati on the Sky as follows:
Thus Krishna had a full ‘darshan’of Shiva accompanied by Parvati, Shri Krishna applauded him as follows:
Namostu tey Shashwata Sarvayoney Brahmaadhipam,
Tapascha Satwam cha Rajastamascha Twaameva Sarvam pravadanti Santah/
Twam Brahmaa Hariratha Vishwayoniragnih Samhartaa Dinakara mamdalaadhivaasah,
Praanastwam Hutavaha Vaasavaadi bhedastwaamekam sharanamupaimi Devameesham/
Saamkhyaastwaam Vigunamathaahureka rupam Yogastwaam satatamupaasatey hrudistham,
Vedaastwaamabhidadhateeh Rudramagnim twaamekam sharanamu- paimi Devameesham
My salutations to You Shaaswata! Sarva Mula Kaarana or the Root Cause of the Totality; Rishis affirm that you are the Master of Brahma; they assert that you are the Spring of the Three Gunas of Satwa-Rajasa-Tamasas; indeed you are the one residing in all the Lokas of Brahma, Vishnu, Vishwayoni, Agni, Samharta and also in Surya Mandala; You are the varied Forms of Praana, Hutavaha or Agni, Indra and all other Devaas; I have arrived into the shelter of Maha Deva;
Yasyaseshavibhaaga- heenamamalam hridyantaraavasthitam
Tatwam Jyotiranantamekamachalam Satyam Param Sarvagam,
Sthaanam praahuranaadi madhyanidhanam yasmaadidam jaayatey
Nityam twaahu –mupaimi Satyavibhavam Vishweswaram tam Shivam/
Om Namo Nilakanthaaya Trinetraaya cha ramhasey,
I seek shelter unto the truthfully glorified Vishweshwara Shiva, whom Tatwajnas worship as he is Indivisible, Transparent, Existent in one’s interiors of heart, Luminous, Infinite, Unique, Stable, Truthful, All-Pervasive displayer of Beginning-Central-Terminating points of Life. My sincere salutations to you Pranava Swarupa, Nilakantha, Trilochana, Shakti Rupa, Maha Deva, Ishaana, Pinaaka dhanush dhaari, Munda-Danda Dhaarana, Vajra hasta dhaarana, Digvastra, Kapardini or Jataadhaari with Matted Locks; Bhairava naada, Kaala Swarupa; Naagayajnopaveeta dhari (He who wears Serpents as the Holy Thread); Agni samaana veerya nidhana (He whose semen is like Fire); Gireesha; Swaahaakaara or of the Swarupa of Offerings to Agni in Homas; Mukta -atthahaasa or He whose maddening voice reverberates...
Maharshi Markandeya wondered as to why Krishna who himself was worship-worthy and granted boons to his devotees worships Shiva Lingam, Krishna replied smilingly:
Markandeya! Whatever you said is in order and the Truth is that I am worship-worthy by others; but still I worship Ishaana; there is nothing that I cannot achieve a thing, nor is unavailable to me; yet I am aware that I perform Puja to Parama Shiva. Those who are unable to overcome Maya or Illusion could never achieve Shiva Darshana; but I do realise that my foundation is Shiva and hence I always worship Him. There is no better Punya Phala nor fearlessness than what the Sacred Task of Lingaarchana would confer and for accomplishing propitiousness human beings must resort to Shiva Puja, Shri Krishna affirms. Those who realise and experience Vedic Siddhaantaas (Principles) do recognise that Shiva Linga is my own Swarupa and that is precisely why I perform my own worship of the Atma Swarupa of Ishana, says Krishna. He further confirms: I am Shankara’s Parama Murti and I am Shankara myself without doubt. Vedas have emphasised that there is no difference whatsoever and Krishna and Shiva are just the same. This is the reason why that one should install Shiva Linga all over
And in a different chapter of the same Purana now Lord Shiva affirms the oneness of Shiva-Vishnu as follows:
In the context of the above, Maha Deva emphasised again as in earlier pages about the identity of himself and Vishnu Deva; this was necessary since a seperate ‘Ishwara Gita’in the current Kurma Purana sought to clarify that its contents were in no way contradictory ; even in the description of Shiva Tandava described above, Vishnu too was stated to have joined the Celestial Dance! Maha Deva thus confirmed as follows:
Ayam Narayano yohameeshwaro naatra samshayah,
Naantaram ye prapashyanti teshaam Devamidam param/
Mamaushaa Paramaa Murtirnaaraayana samaahvayaa,
Sarva Bhutaatmabhutasthaa Shantaa chaakshara sangjnitaa/
Ye twanyathaa prapashyanti lokey bheda drusho janaah,
Na tey maam samprapashyanti jayentey cha punah punah/
Yetwimam Vishnu – mavyaktam maam vaa Devam Maheswaram,
That Narayana is Ishwara that is me undoubtedly. There is indeed no difference between us and he too is to be worshipped. Narayana is ‘Shaanti-Akshara’ imprinted in every body’s heart. Some imagine otherwise that we are figured other wise and they continue to get into the cycle of birth and death and could never ever attain Mukti. Those who visualise me and Narayana as just the same would have no rebirth. As such, Vishnu has no beginning or end as in my case, meaning thereby we are both the same. Those who confuse Vishnu as another Deva would for sure reach Narakas. Those who are my bhaktaas being either Murkhaas or Stupids, Panditas or Learned Vidvans or even untouchables should indeed have the possibility of Mukti, provided they do not dislike or distrust him. Hence my bhaktaas ought to perform puja to Vishnu with all humilty and belief.) Then both Vishnu and Shiva disappeared simultaneously, stated Vyasa Muni.
Thus both Lord Shiva and Lord Vishnu (in the form of Krishna) affirm the one-ness of Shiva-Vishnu in the same Purana. So, you can verily be the devotee of one God and see the other God just as another form of your Ishta (favorite Deity).
To sum up, i am quoting few verses from an Agama called Nila Tantra, which is part of another major Agama called Vishnu KrAnta:
TAvat Tantre Bhedabuddhi Stavadeva Prithak KriyA | Harihare BhedabuddhirjAyAte Jagadambike ||
KarAlavadana KAli Srimadekajata ShivA | Shodashi Bhairavi BhinnA BhinnA Cha Bhuvaneswari ||
[Lord Shiva says] As long as Bhedabuddhi ( the feeling of dvaita or duality) is there, the rituals and methods are different for different devotees. [Then] There appear differences between Hari (Vishnu) and Hara (Shiva). It appears [then] as if KAli, TArA (Ekajata), Shodashi, Bhairavi are different different...
Nila Tantram 22-9.11