irreligious man

“I am an irreligious man but I think, that everyone should respect other feelings and beliefs.”
Is this sentence correct?

“an” is correct but the comma is not.

I think it is not so common for people to self-describe as “irreligious”. It would be more usual to say “I am not a religious man”.

Should it be others feelings and believes?

No, “believes” is a verb. In this case a noun is required.

“others” is also incorrect. This would be correct: “… others’ feelings and beliefs”.