Well, the Dvaita and the Vishisthadvaita philosophies is not specific to the Vaishnavites alone .They are prominent in the Shaiva-Shakta philosophies as well. Shaiva siddhantis or Tamil siddhantists accept four types of Mukti : salokya, saamipya, saarupya and saayujya. Sajujya means attaning Shivatwa, but NOT becoming one with Lord Shiva. So they are Dualists. According to Sreekantha, Shiva is both same and different from Shakti, like Moon and Moonlight. Thus this view is similar to the Achintyabhedabhedavada. Sripati says Shiva is like spider and the world like its web. So its similar to the Vishistadvaitavada. Sripati says that Shiva is both the upadana karana and nimitta karana of this world just as Ramanuja says about Brahma.
There are tantric yantra, and manra to worship Sri Krishna that the Vaishnavas use .The Vaishnavas generally follow Sanatkumartantra, Gautimiyatantra, Saradatilak, Naradapancharatra and Kramadipika. Nirvantantra also describes the process of worship of Radha and Krishna. Brahmandatantra says that Mahashakti is worshipped as Krishna and Vishnu. Gautamiya Kalpa says- Krishna and Durga are one. The one who sees them as two can not be liberated (This sloka was quoted by the famous Gaudiya Acharyya Srila Srijiva Goswami).
According to Mahamahopadhyay Gopinath Kaviraj, all types of sadhana are tantric sadhana, as all the Vaishnava sects also have their own tantras. (Ref: Shastramulak Bharatiya Shaktisadhana, Upendrakumar Das, Vol 1 and 2).
I am now answering to the last part of the question.No, real Vaishnavas are not reluctant to accept all vamamargis and Kaulas.Srimadbhagatam says that there are thtee paths to worship the Supreme : Vedic, tantric and a mixture of these two.The great shakta saint of Bengal, Sri Kamalakanta Bhattacharyya was disciple of a Vaishnava Goswami saint. He composed songs on Sri Krishna, Sri Chaitanya and on unity of Krishna and Kali. The famous Vaishnava saint Sri Ramdas Kathiababa was a very cery close friend of Sri Bamakhepa, who was a famous Kaula. Mahaprabhu Nityananda was an Abadhuta, ie a tantric monk, who regularly worshipped Shiva and Shakti.Sri Radharamana Charandas Babaji received spiritual instruction from Goddess Durga. Sri Bijaykrishna Goswami, the famous Vaishnava saint respected Sri Ramakrishna and Sri Trailanga Swami very highly and both practised Tantra.
All debates end when realization starts.