(Righty, but have played both cello and guitar).
For most people, there is a difference between playing left-handed and right-handed: McCartney, Hendrix and others didn’t play left-handed just to be different or weird. I remember an interview where McCartney was saying he could play guitar passably right-handed, but just couldn’t get the ‘funky’ strumming rhythm that he could left-handed. For a lefty learning guitar, I’d suggest trying righty for a while, and then lefty, in order to see which is better for that person. You don’t need two guitars for this: An regular acoustic guitar re-strung to play lefty might not sound quite as good, but will be good enough, and electrics will sound the same either way (the only difference righty and lefty is being able to finger the higher frets; not necessary when first learning).
Unfortunately, playing lefty is not really much of an option for learning classical strings. If you’re playing in an orchestra, you’re going to play the same side everybody else does. Maybe, somewhere, in some super-alternative elementary school, there’s a conductor who’d be OK with one of her players doing everything backwards and is willing to rearrange seating to give the student the extra space they’ll need, but don’t count on it at any higher level. However, I don’t think the left-right difference is going to be as pronounced with classical music, where the rhythms are simpler.
If the student’s only goal is to be a bluegrass fiddler, I suppose it’s more possible. Left-handed violins are hard to find, and playing a normal violin left-handed will not sound as good (but probably close enough for bluegrass). Not every classical teacher will be willing to teach left-handed, but some might, and if you’re just getting a fiddle teacher, more likely.