I've set stools with a very "slight" sobble on dry fit with no shims.
Once the wax ring and Johnny bolts are in place, the wobble was gone.
Could it leak? Maybe. Could it break the porcelain? I suppose. But
I've had neither. Remember, I'm talking about a very slight wobble.

On occasions I had to shim and used shingles (improvising on
construction sites).

I would shim it with something like the plastic shims available at HD
or Lowes. Thin set might give you issues when replacing the toilet in
the future. I don't think the foam would be solid enough long term
and you do run the risk of "lifting" the toilet from the wax seal if
you use too much.