Will sewing onto neoprene compromise its water resistance?
If you're starting with waterproof neoprene (which may be closed cell or coated on one side), thread holes will breach this and it will leak.  It would be unlikely to let light rain in but putting it down in a puddle would allow it to leak.

I have a neoprene laptop case, and it's not the waterproof type of neoprene, but if any water (rain, or from wet things in the same bag) gets in it's around the stitching.  You're also likely to have to look hard and pay more to get a waterproof case, whether or not it's neoprene.

You should be able to seal up the holes though, with neoprene repair glue (wetsuit glue, "neoprene queen" is the brand I use).  This may be worth it even on a non-waterproof neoprene case. This is discussed in a question (mine) on outdoors.se How can I adjust a neoprene wrist/neck seal on a drysuit, by cutting and joining?.  My own answer after trying it has some ideas, including blind stitching.