How many things do we all do in a day that we don't care for because someone else would like it?

False equivalency. There are also lots of things we won't do even if someone would like it. Etc.

Do you refuse to go to weddings and funerals as well because they're held in churches,

Again, a false equivalency. Attendees at a wedding are NOT de facto assumed to be members of that church or even of that religion. This is why Christians attend Jewish weddings and vice versa without any presumption that they are adherents or devotees.

In your example, no one is lying to anyone about anything. Attendees are simply showing their respect for the happy couple and whatever belief system they have. And they're allowed to wear their cross necklaces, state they just came from temple, etc.

I'm sorry, my view of the world is not as black and white or rigid.

It's really not a matter of "world view". It's about your own personal integrity.

A far better analogy would be the dying woman (and/or the family) asking her daughter to break up with him because he is black...but just until she passes away. You know, to make her feel better.

Would you still disagree with my stance if this were the case? Because my position wouldn't change.

She's on her last legs and it would make her happy.

Since the odds are quite high that she already knows OP isn't religious, then the only way this "makes her happy" is that her little guilt trip/power play/manipulation "wins". In the extreme case of this, which I have seen in action many times in my life, that's a very sick person at their very core. Hopefully, she's pulling more of a "little white manipulation". ;)

Is it really worth it?

I didn't say it was easy. Lying, even a little white one, is often the shorter, easier route through a problem...which means that it can be an act of selfishness, or laziness, or even outright cowardice to avoid taking the time to act truthfully.

But I also made it crystal clear that he does not need to turn the spotlight on his lack of belief. Refusing to discuss the matter, as this is clearly not the time to do so, is sufficient to get the point across without engaging.