"It is completely unacceptable to me as a theist to allow people who don't believe in a god to legislate morality based on their own personal feelings."
Would this be fair? Why or why not?
There is a fundamental difference. The legislators who are acting on their own morality can be held accountable for that morality, since it is theirs. If their morality is unacceptable to the governed, then they can be removed (by whatever method is available in the government in question) and replaced with more acceptable leaders.
A theist lawmaker who legislates based on what is supposedly divine decree, cannot be held accountable for that morality, since he or she is "just following orders" and his or her (dis)agreement with said decree is irrelevant.
The latter works well in an absolute dictatorship, where nobody can hold the legislators accountable anyway. The former is much more suited to modern representative governments, such as democracies.