Does completing one's ablution after seeing a picture of a church on a shirt constitute an act of apostasy?

It is clear that obsessive whisperings have taken a toll on you. It is incumbent upon anyone afflicted by them to disregard them, occupy themselves with what benefits them in their religion and worldly life, make abundant supplications, seek the removal of affliction, request legal ruqyah (exorcism), and consult doctors. There is nothing in what you mentioned that would cause one to exit the fold of Islam. However, if the garment bears the sign of a cross or a symbol of disbelief, wearing it falls between being disliked (makruh) and forbidden (haram).