There is a very small minority of people who put on the headset and immediately can't stand it. I've seen maybe 2 or 3 people in the last 6 years, so it's definitely less than 1%.
Depending on content, I've seen about 50% of women and 25% of men experience mild discomfort after using the headset for about 30 minutes. Studies on simulator sickness include that in "feeling sick".
My current project is not able to use every single sim-sickness mitigating strategy available, due to the sort of source data we're using (a lot of flat, 360 imagery in a multi-user tour-like scenario), but even there, we've only had 1 out of 100 people express actual feelings of nausea after using the headset. If people report any discomfort at all, it's on their first time, after they've not heeded our warning to limit their first interaction to 30 minutes, and then they only mention feeling a little light headed.
People report feelings of nausea after playing 1st-person shooter video games on large screen monitors or watching shaky action movies at movie theaters. This is not a problem unique to VR.
There is a problem though with a lot of crap games not implemented with comfort in mind and badly optimised. Stuttering will get you feel bad fast.
OTOH, considering how many people keep having motion sickness in cars (especially when not driving and reading and whatnot), perhaps for some people the issues remain.