In my limited experience, I'd say that anything over a difference of 0.01"+ is getting to be 'loose'. The pieces tenon should be able to be inserted into the mortise by hand, that is to say does not need to be hammered in.
But it should have enough friction that it does when dry fitting that the tenon piece does not fall out of the tenon.
If it is looser AND it truly needs to be blind, then I would recut. If you don't mind visible dowels or similar, It would not be unheard of to convert it to a doweled/pegged mortise and tenon joint. Personally, I think they are similarly beautiful, and can add interest if you dowel/peg with a different species of wood (contrasting color like maple and oak, or poplar and mahogany are personal favorites). In the photo below, they were adding manufactured dowels, but scraps of contrasting hardwood, or simple cut dowels could be exchanged.