This could be a general question, but it may make a difference that the person involved is a co-worker and not a friend or family member, so I put it here instead of Life in General.
Ann is a co-worker that I am somewhat friendly with (we will chat back and forth a little from time to time) but that I wouldn't consider a friend at this point, for unrelated reasons. She sits in the cubicle directly across the aisle with me.
Betty is a co-worker that I would consider a friend, and have some contact outside work. Not a fully social friend, but maybe a "work friend". Her cubicle is directly in front of Ann's.
(If it matters, I did used to interact and chat with Ann more, but there have been a couple of incidents that have inspired me to back off a bit on any conversation that is not necessary, but it's hard to halt that completely with Ann who sits next to you without causing unneeded drama while still being sociable with Betty in front of her. I did try it for a bit, but it felt like when you are trying to talk around the person seated next to you at a table.)
Story and questions:
Not too long ago, Betty asked me, away from our desks, "Why do you still say 'Bless you' when she sneezes? She never says 'Thank you' to anyone for it, and never says 'Bless you' to anyone either." I replied that I say 'Bless you' to everyone; it's a habit and a polite thing to do. Since then, I've paid attention and Betty is right. Ann never says 'Thank you' when someone says 'Bless you' to her, and never says it to anyone else.
1) Is it rude to not say 'Thank you' when someone says 'Bless you', or acknowledge it in some other way?
2) Is it rude to say 'Bless you' to everyone in a group except for one person? Does it make a difference if that person has never acknowledged a 'Bless you'? (Note: There are other people besides me that still 'Bless you' Ann, but I don't know if she would notice even if there weren't.)
3) Is it rude to never say 'Bless you', 'Gesundheit', or sneeze-related comment of your culture when someone sneezes?
4) Do the answers to the above questions vary based on whether the person is close (friend, family member), not-so-close (co-worker, acquaintance) or complete stranger?
Bonus question: Was Betty rude with her question and comment?