I believe that if I expect people to respect my right to be an atheist, then I have to respect other people's right to believe as they do. Do you agree?
Agreed.
Belief happens in someone's head. No one can interfere with my life, liberty, or pursuit of happiness from their head.
Hands, feet, mouths, ballots, and legislations are a different--stickier--story...
Bottom line: no one can get inside my head and make me believe anything, just like I can't get inside anyone's head and make them not believe something. The external, physical world is where we need to get along--and that begins with respect.
Another way to look at it with different phrasing... Your thoughts, feelings, and opinnions are yours alone. No one has the right to tell you what you should think, feel, or believe. You are the only one who can change what you think, feel, or believe.... and you do not have the right to tell others what they should think, feel or believe. They are they only ones who can change those things. Certainly all parties could have a discussion about their beliefs, but condemning another or feeling superior during those conversations wouldn't be welcome.
Its necessary to respect that the individual has a belief, but you don't necessarily have to respect the belief of itself.