Various sects would have own views regarding this. Vaishnavas might tell moksha is not possible without grace of Lord Vishnu, similarly Shaivites might tell it is not possible without grace of Lord Shiva and similar for other sects like Shaktas, Ganapatyas, etc..
However we can take help of Shruti verses or eternal Veda sentences in such cases:
1) Lord Shiva:
There are various answers here which state Lord Shiva can't grant moksha. However this is not statement of Vedas, it's their own imaginations.
Lord Shiva is the only God in Samhitas of Vedas from whom the revealed mantras during meditations ask for Moksha. RigVeda 7.59.12, Taittariya Samhita of YajurVeda in 1.8.6.i, Vajasena Samhita of YajurVeda in 3.60 declare the same statement as:
त्र्यम्बकं यजामहे सुगन्धिं पुष्टिवर्धनम्
उर्वारुकमिव बन्धनान्मृत्योर्मुक्षीय माऽमृतात् ।।
We worship the Three-eyed Lord who is fragrant and who nourishes and nurtures all beings. As is the ripened cucumber freed from its bondage (to the creeper), may He liberate us from death for the sake of immortality.
= मृत्यु + मोक्ष + मम अमृतात्
ie. Moksha through death for immortality.
And also 10.17 of Taittariya Aranyaka of YajurVeda clearly declares:
सद्योजातं प्रपद्यामि सद्योजाताय वै नमो नमः।
भवे भवे नाति भवे भवस्व मां भवोद्भवाय नमः॥
I take refuge in Sadyojata. Verily I salute Sadyojata again and again. O Sadyojata, do not consign me to repeated birth; lead me beyond birth, into the state of bliss and liberation. I bow down to Him who is the source of transmigratory existence.
So, it is purely imagination of persons who think Lord Shiva can't grant Moksha.
The same fact is repeated again and again in Smriti passages like:
For eg. In Anushasana Parva of Mahabharata Devas pray Lord Shiva as:
शक्रोऽसि मरुतां देव पितृणां धर्मराजसि ।
ब्रह्मलोकश्च लोकानां गतीनां मोक्ष उच्यसे ।।
You are Shakra among the Marut Devas, Dharma among the Pitris, Brahma Loka among the Lokas and Moksha among the paths (gati).
As Lord Shiva is also known by the name Bholenath, he readily grants Moksha out of compassion of beings. One of the such place is Kashi. Thats why even the Srimad Bhagvatam tells Kashi as best among the holy places.
क्षेत्राणां चैव सर्वेषां यथा काशी अनुत्तमा ।
तथा पुराणव्रातानां श्रीमद्भागवतं द्विज ।।
Just as Kashi is the best among the holy places, in the Similar way Srimad Bhagvatam is best among the Puranas. [S.B. 12.13.17]
Srimad Bhagvatam tells Kashi as best among the holy places because it is that place where Lord Shiva readily grants Moksha. Kailash Samhita of Shiva Purana in 3.2 states:
अतस्तदेव जानीयात्प्रणव सर्वकारणम् ।
निर्विकारी मुमुक्षुर्मां निर्गुणं परमेश्वरम् ।।
एनमेव हि देवेशि सर्वमन्त्रशि रोमणिम् ।
काश्यामहं प्रदास्यामि जीवानां मुक्तिहतवे ।।
Hence he who aspires for salvation and is free from aberration shall understand the Pranava as the cause of all, and Me as the Nirguna Parameshwara. I give this crest-jewel of mantras at Kashi for the liberation of all individual souls.
So, it is clear from both Shruti and Smritis that Lord Shiva grants Moksha. Moreover in the Shiva Purana and Skandha Purana and in many other Puranas there are many stories and events where Lord Shiva provides moksha and it is not that Vyasa fakely claimed in Puranas that they attained Moksha.
2) Lord Vishnu:
I am not aware of any Vedic Samhita mantras that ask for Moksha from Lord Vishnu. Maybe there are in Brahmanas and Upanishads (one can inform me if he/she knows).
However this doesn't mean that Lord Vishnu can't provide Moksha. Moksha provider of Vedas ie. Lord Shiva himself states that Lord Vishnu is the God who grants moksha.
In the Harivamsha Parva, Lord Shiva tells to Ghantakarna:
मुक्ति प्रदाता सर्वेषां विष्णुर्वे न संशय ।।
There is no doubt that Viṣṇu is the deliverer of liberation for everyone.
Lord Shiva himself didn't gave Moksha to Ghantakarna because he used to severly hate Lord Vishnu. He used to tie bells in ear so that he may not be able to hear name of Lord Vishnu and thus his name became GhantaKarna. Due to extreme hatredness towards Lord Vishnu (Virodhi Bhakti) he became eligible to get moksha through Lord Vishnu and later Lord Krishna gives him a boon that he would attain Sayujya with Vishnu after period of present Indra is over as I discuss in my answer here.
Also in Bhagvad Gita 18.66 Lord Krishna states:
सर्वधर्मान्परित्यज्य मामेकं शरणं व्रज |
अहं त्वां सर्वपापेभ्यो मोक्षयिष्यामि मा शुच: ।।
Abandon all varieties of dharmas and simply surrender unto me alone. I shall liberate you from all sinful reactions; do not fear.
And also from various stories of Vishnu Purana, Padma Purana and Harivamsha and other Puranas we can know Lord Vishnu provided Moksha to various persons.
3) Advaita type:
And in the Advaita type moksha, even if a person reaches Parampadam of Vishnu or Sadashiva Loka of Lord Shiva, still he may not be Jeevan mukta. However he won't return from there as Lord Krishna tells in Gita " those who have attained my place do not return." and hence their Jnana is granted. However as they are still under Nama-Rupa they maynot be JeevanMukta. They still need Jnana to realize oneself as the Supreme Nirguna Brahman without any forms and attributes.
So, in Advaita God doesn't directly give moksha, or devotion doesn't directly provide moksha. God provides Jnana which will finally make one Jeevan Mukta. And Jnana can also be provided by Guru.