I'm lucky enough that I don't have much scars on my hand because in middle school I switched to my legs instead, because I was worried about future career. However - there are are some pretty big white scars, so basically - if someone notices them, they can quickly puzzle it out (I have had such situation with perverted lecturer at my university + a lot of friends asked questions).
I try to keep it hidden at work. It's quite inconvenient, since I've just started a work and we have temperatures about +/- 30 C (90 F) right now. But I work in an office that is air-conditioned, so it's easier to wear a jacket. Except the day the air-conditioning broke down
However, since I've got some little, but quite fresh red scars that really catch the eye - it's better that way.
And well, to be honest - I think hiding it is a really good idea. I was rejected university team-project due to my problems. The coordinator said it was better if I didn't work in group, because I was right after release from psychiatric hospital (and had to inform university authorities about that). So well, I don't think I would once again let my mental issues influence my career.
On the other side - I quite of understand the approach. I mean - if you were to decide who to hire and had two people of similar qualifications to choose from - wouldn't you rather choose the one without mental issues? It's kind of a deal, since you cannot predict if and when such a person would break up nervously. And if someone is mentally disturbed - there is a bigger change that their problems would impact the efficiency at work.
You can say it's not fair, but also - the life isn't fair as well. If you want to be taken seriously, then do whatever to look like a professional. Fake it, till you make it.