Wall stud spacing too tight for replacement medicine cabinet

1/8" total? That's 1/16" on each side. Sand it down and call it a day.

Spread the studs slightly by banging in place 2x4 blocks 14.5” long these will become the new top and bottom of the opening.

Sanding could work, but it a tedious job. Try this first: mark the top and bottom of the cabinet on either stud. with a saw or chisel cut a line on the inside face of the stud (top and bottom).

Using a chisel plow out the wood in between the two cut lines. It should chisel out quickly and not produce alot of dust.

A viable alternative is to consider returning the cabinet, and buying a narrower one instead.

Or slightly modifying the new cabinet by shortening the top/bottom plates and any back panel so it fits the available space, and the 1/8" overhang becomes part of the opening (ie you don't have to faff around with hinges) This presumes its wood or similar, and not a blow-moulded plastic part.

Considerations: Using power tools will shake up the wall a bit and sometimes cause the drywall nails to appear or cracks and things so you end up refinishing and repainting. So prepare for that. You could use an orbital jigsaw and trim out what you need on each side so it's a nice easy fit without spreading the studs which might cause nail pops over time up and down them. Or, if you are careful, a cut with a worm drive skillsaw starting with a plunge cut on each side but don't cut yourself doing this if you are not a tradesman. Sanding would take forever. If you don't mind exposing studs and what you need and are skillful at drywall repair and wood work, then you could just frame it as you need. *** How much depth do you need?