Entering a church

Is it permissible to enter an ancient church on a tour in order to observe ancient works of art, etc.?

Answer: It is forbidden to enter a church that is in use as such, even to see works of art, even if it is for the purpose of peace with gentiles.
If an ancient church is being used only as a tourist attraction and museum, then the matter depends on the profit being made. If the profits go to a private body and not for religious purposes of idol worship, (Christianity for example, is considered idol worship according to Halacha,) then there is no prohibition against entering.
In any event, it is preferable to avoid it because of the prohibition of maarit ayin, meaning that people could see and infer that it is permissible under other circumstances or under any circumstances.