I am swapping out a toilet. The old toilet, a round bowl with a squared front, was shimmed like crazy to get it perfectly level. I dry fit the new elongated bowl toilet to the flange to see what I was up against with getting it level. The toilet sits perfectly flat on the tile. It does not rock. It is level from side to side, but is un-level front to back. To get the toilet level front to back I would have to raise the front approximately almost 3/8". The flange itself also is level side to side but tilts slightly forward front to back. If the toilet sits flat, do I really have to make it level front to back? I also am going to use an extra thick wax ring with the plastic collar to help ensure a good fit. Does this sound appropriate?
There are purists out there that may say it must be level, but if it looks good setting there, I would let it set on the floor with no shims. It should not affect the operation of the flapper or valve that flushes the toilet. I would rather see a consistent caulk line at the base of the toilet than it setting level in both directions and have a huge joint in front.
This depends a lot on how the toilet is built. I recently installed some new Kohlers and, with the new EPA mandated 1.28 gpf, I've noted the water is channeled to the front of the chute. This pushes the waste directly out. I doubt a toilet like that would be affected by front-back leveling. The real question is if the new toilet channels a lot of water via the rim. I've seen some where the water is sent through the rim to the front of the bowl, where it comes out a larger opening. This produces a natural "thrust" as the water comes down the bowl. If your toilet tilts back some, it could interfere with this, turning a one-flush into a two-flush.
If I were you, I'd just shim it level. It's annoying but you avoid any questions. A set of plastic shims is cheap (like $3 at your local big box store). If you want to just put it in as-is, I'd give it a test flush with something to simulate solids in it (or just deposit your own) and make sure it has the power to push it down