Some people yes, others no? Contacts would seemingly help, but you're still going to have a build up of acid in your eyes that could eventually become irritating with enough volume.
I've known people who just have seemingly no reaction to onions whatsoever, and others who break into tears the second the first cut happens.
Yeah ymmv, but to me it's night and day - with lenses I'm in your first group, without them I'm in the other. Of course I've never cut more than maybe 20-30 onions at a time, but I never felt much of anything doing that. A single cut without lenses on had my tears flowing instantly. I finally got what all the fuss was about - turns out it's not fussing at all. :)
I've known people who just have seemingly no reaction to onions whatsoever, and others who break into tears the second the first cut happens.