Are the Telvanni at all religious?

In-game, House Telvanni is the only one of the Great Houses that has a negative disposition towards the Tribunal Temple, and it is made evident upon investigation that in the Telvanni territory on Vvardenfell there are no significant temples (I can only think of the miniscule chapel in Vos and the one in Sadrith Mora which besides being small, it is sort of hidden very deep underground).

What is it about the Tribunal Temple that does not appeal to the Telvanni? Do they take a more Dwemer approach to religion or do they hold on to Ancestor worship?

Lord Telvanni considers his last child to be a gift from Azura in his journal (Brand-Shei's quest in Skyrim). Of course, he was under extreme duress at the time. I don't think the Telvanni were so much anti-religion as they simply couldn't be bothered with it.

I'd say this is about right. Master magisters have no time to dabble with the worship of gods, especially not the Tribunal, who after all are merely Chimer using the power of the Heart.
Daedra worship, maybe, but not zealously so.

Yup. I'd add that they're likely against the institution of the church rather than the actual religion. They're not going to deny that Vivec is a god, but they're likely not fond of all the rules about necromancy.