Some tenet

I don´t know if this sentence is correct: "My main tenet is always to listen to other people".

 I believe you are making a statement about your tenant who always listens to other people. If my assumption is true, you will have to say

"My main tenant always listens to other people"

"My main tenant always listens to others"

Some tenet

I don´t know if this sentence is correct: "My main tenet is always to listen to other people".

Yes, this is correct.  But it would be more common to say "my main principle..."   Tenet is  more formal and here it sounds like a quotation from a book.