That I can't do religious stuff! I don't have to believe in the religious components to participate in an event that holds meaning to you. To me it's not sacred -- all just normal words being said and ordinary matter being handled according to some rules. I do that every day at work at the direction of a different kind of "higher power" (clients) without anger or discomfort, it's really not a big deal!

I'm not angry at god for not existing, nor am I angry at all the people who believe otherwise. If the invitation to your religious event is in good faith, I'm honored to attend, and will just keep to myself or make small talk. Plus I've studied enough faiths I can probably fake it, if keeping the situation under control requires it ;)

I've discovered that in practice, many people of different faiths are not sure what to think about this position. Most are OK with it, some not (I just give them their space). With the interesting exception of Buddhists! They've always been super excited to bring me along to the pagoda somehow. No one ever tried to convert me, and the monks often speak a surprising number of languages and are interesting and well traveled. It's become a set of surprisingly wholesome memories (I immigrated to a primarily Buddhist country)!