This thread talks about "handedness" and I did a post on the 2nd page about lefthanded violins which I think/hope is reasonably factually correct.
IMO, and I am no expert, lefthanded playing is fine if the player knows they won't ever want to play in an orchestra and doesn't mind continually having to search for appropriate violins. As Allan says, one that has been "swapped" is not truly a lefthanded violin and won't perform as well as it should because it wasn't made to be played that way round.
...If you're interested,
this is my take on the subject... I will stress that I am no expert, not even marginally, but personally I can't help thinking that the complexity required of both hands, and the unnatural posture etc, suggest that which way round you play a violin won't make that much difference - both hands need to be reasonably dextrous and skillful, and it's going to be difficult anyway! - and I don't think the advantages would outweigh being unwelcome in orchestras (yeah it's a symmetry thing, but also having all your fiddlers and other sideways instruments the same way round makes arranging your sections a heck of a lot easier!!

) & limited choice of instruments. I know at least one lefthanded studying strings "righthanded" at music college, and apparently Paganini was lefthanded too... draw your own conclusions

- that's just my deeply inexpert take though, and maybe lefthanded violinists will become less rare if students start getting taught that way...