how critical are distances between studs?
Not critical at all.  There are best practices.  Like making sure corners have stud surface on both sides, making all studs 16 on center, make all studs plumb.  Does it matter?  No.  Do inspectors care?  No.  Now I wouldn't suggest making your studs further than 16 inches but back in the day they were generally 24 for basements.  I have seen people do them at 12.  The only concern that you should have is when you drill the drywall in, is the stud in question going to cause issues...

But if it were me I would just whack it back in place.

Note: That my answer here is given that it is a non-loadbearing basement wall.  If the wall was a loadbearing wall or attached to a loadbearing wall it would differ a bit.  In a basement the framing is just space to put insulation, wires, pipes, and an attachment point for drywall.