Do left handed violinists play in orchestras?
Well... I do... (cello).
I don't think I've ever seen any orchestra that uses left handed violinists
It sure isn't a common sight. The vast majority of lefty players plays right-handed regardless. And that's not without reason, because
My guess is that they would clash with the rest of the violinists, and they would seem out of the flow with the rest of the musicians.
Yup, it's definitely a bit awkward. I've gotten quite used to always watching out for my neighbours' bows and doing “evasive maneuvers”. Often feels like making life harder than it needs to be.
“Out of flow” may also be an issue, though perhaps less with violin/viola than with cello/bass, because they bow in fact more up/down than left/right, and are in that sense somewhat parity invariant.
Violinist playing lefty will thus indeed have a harder time finding an orchestral job. In somewhat alternative emsembles or amateur orchestras it should usually be accepted though, there aren't “regulations” against it. I doubt there are officially such regulations even in traditional professional orchestras, but it might still be virtually impossible to get a job in one of those when playing lefty.
Where you find such players more commonly is in folk, where synchronised bowing isn't a thing anyway. One great example is Kimberley Fraser, who with her left hand does some of the finest bowing work I've ever heard.
Whether it is playing-wise benefitial for a lefty to play the other way around is a matter of debate. Many people argue that “in standard playing, the left hand actually does the more difficult job, and therefore right-handed playing is in fact better-suited for lefties”.
I think that's missing the point though: dexterity isn't about “one hand is better than the other”, it's about what tasks each hand specialises in. In most manual working processes, both hands are involved; they need to do division of labour. The “strong hand” may do the actual “actions”, but the “weak hand” is just as important for fine-aligning and keeping the working material in place.
And that is much the same thing in string instruments: the right hand (for a righty) gives the rhythmic and dynamic impulses, whereas the left hand makes the conditions for this to be musically useful, by fingering the right notes/chords.