My mother is afraid of crowds. Should I let her miss her sister's funeral?

I'd keep in mind that with Alzheimers, the patient loses the ability to process information and regulate their emotions. Being around crowds of people can be frightening and she may become inconsolable. I'd discuss this with her doctor, before insisting she do anything that she doesn't want to do.

I can understand your Mom being afraid of crowds, as I have a mild case of agoraphobia.   With agoraphobia the person's senses get overwhelm... people milling about... the noise level starts to climb and you start to feel panicky.... then you feel like you have disappeared into the crowd, and what will you do when you faint.   These feelings are all real.

What you can do is take Mom to the funeral visitation, maybe Mom will make a brave attempt to go inside.   Keep reassuring her that you will be nearby in case she wants to leave, and you promise you will leave, not try to convince her to stay.   If she knows there is an "out" she might go to the visitation, even if it is only 5 minutes.   Even sitting in the car is a safe haven for her.

One thing, have Mom drink a bottle of water just before going, as dehydration can also mimic a panic attack.   Some times just going into the funeral home bathroom when feeling panic will help as it becomes a distraction for Mom.

With Alzheimers, I would go with whatever she wants. If she senses that she can't handle it, then support her decision fully and move on. I would encourage her to be content with her decision and that everything is just fine. I wouldn't worry about regret, since she will eventually forget that she didn't attend or perhaps that her sister even died.