I remember reading that Madhwas don't believe Sri-vaishnavites would achieve moksha. I also remember reading right on this board Sri-vaishnavite theories as to how people worship other deities for many births until being born vaishnavite to achieve liberation.
Both pro and con opinions regarding other sects able to provide liberation are available.
Sri Ramakrishna, for example, says that all sects are paths to God.
“With sincerity and earnestness one can realize God through all religions. The Vaishnavas will realize God, and so will the Saktas, the Vedantists, and the Brahmos. The Musalmans and Christians will realize Him too. All will certainly realize God if they are earnest and sincere.
Some people indulge in quarrels, saying, ‘One cannot attain anything unless one worships our Krishna’, or, ‘Nothing can be gained without the worship of Kali, our Divine Mother’, or, ‘One cannot be saved without accepting the Christian religion.’ This is pure dogmatism. The dogmatist says, ‘My religion alone is true, and the religion of others are false.’ This is a bad attitude. God can be reached by different paths.”
The Gospel of Sri Ramakrishna, Chapter 8, The Master's Birthday Celebration at Dakshineswar, March 11, 1883.
Certain Puranas express the exactly opposite view. Garuda Purana wages war against non Vaisnavas.
I abhor the non Vaisnava people and love the Vaisnava ones. I cut off the tongues who reproach Lord Vishnu. With the heated liquified tin I fill the ears of those who hear his reproaches.
Garuda Purana, Bramha (Moksha) Khanda, Chapter VI
Siva Purana is not so strident but it makes it clear that Vishnu attained his eminence because of the good wishes of Siva. Siva is Isvara and not Vishnu.
The Lord taking up a visible form in order to chastise Brahma who practised trickery, came out of the column of fire. On seeing the Lord, Vishnu stood up and with his hands shaking with fear caught hold of the lord's feet.
It is out of ignorance and delusion about you whose body is without a beginning or end that we indulged in this quest prompted by our own desire. hence O, Sympathetc Being, forgive us for our fault. In fact, it is but another form of your divine sport.
31." O dear Hari, I am pleased with you, because you strictly adhered to truth in spite of your desire to be a lord. Hence among the general public you will have a footing equal to mine. You will be honoured too likewise.
Hereafter you will be separate from me having seaparate temple, installation of idol, festivals and worship."
Thus, formerly, the lord was delighted by the truthfulness of Hari and offered him a footing equal to his own even as the assembly of devas was witnessing the same.
Siva Purana, Vidyesvarasamhita 7.29-33