1- Everyone has the right (for-with-to-in) their own beliefs.
I will choose (to) but the meaning of the sentence isn't clear,right?
**Neither a teacher nor a native speaker.**
Right to = verb.
It's not like: "to + verb"
Everyone has the right to live their own life.
Everyone has the right to their own life. -> Similar to your sentence.
(I changed the sentences a bit, but only to show you the "right to" difference.)
Not a teacher.
There is an implied "have" or "hold" as in "everyone has a right to (have/hold) his own opinions."