How much play in a spring suspension fork is normal or safe?
It doesn't sound like it's dead yet.

Play means that the bushings are worn out.

If you continue to ride it just how it is, you will end up damaging the stanchions. However, it is not dangerous to your personal safety to do so.

Replacing the bushings seems like the best option. I doubt the stanchions have any damage if it's only a tiny bit of play like what you're describing.

It is also worth noting that the responsiveness of the fork (how well it "floats") would likely be much improved if you gave it new lube and bushings.