Rocking toilet

I am NOT a plummer, but: I had the same thing twice. Once I installed a toilet in a new house and used plastic shims bought at hardware store. Second time in a recent new house had to put shims in. Toilet WAS NOT LEAKING, just rocking. Just loosen bolts a little, careful not to break seal of wax ring, and slip shims under then calk and tighten.
The flooring people either accidentally or other knock these shims out when they are in their way. Irritating but not a big deal.

Bob- the toilet should not rock, period.
The new tile – how thick 1/4″ or more?
On concrete or wood floor?
If the toilet rocks, call the tile contractor and complain that the new floor is not level. (Unless of course you are using Mexican tile, Saltillo or other which is always uneven.)
While I hate to shim toilets, I have done it using either brass or plastic. The trick is to get the shim under that appropriate spot with enough width that even if it moves it will still support the narrow toilet edge. Good luck.

Try grouting around base of bowl with either Plaster-of-Paris or tile grout. Either will work, just give it time to set up before anyone sits on toilet.

Hey Art, you’re in my neck of the woods.
Respectfully, I would not advise a grout or plaster of paris leveler.
The bowl has a less than 1/2″ lip around the perimeter of the base where it contacts the floor. Any masonry product will , in my experience, not hold up under those thin (1/16 to 1/8 high and 1/2 wide) conditions.
The stool may be stable today, but won’t stay that way as the thin base crack out.

I must agree with Tom. I’m not an advocate of ever grouting, or even using a silicone seal around a toilet base. If the wax seal is ever disturbed, the leak could ruin the wood underneath before anybody sees a leak. jeff