At a recent wedding, a non-member bowed at the altar. Why? It offended me to see it as a non-member, because I feel like I should not have to bow because I don’t believe in it.
I assume you mean that at a recent Catholic wedding you attended, a non-Catholic guest bowed to the altar. Non-Catholics are free to do this if they wish, or they are free to refrain. But they have no reason to take offense when other non-Catholics choose to do so.