Installed new tile floor without removing old toilet flange. Toilet flange is now 1/8" above the floor. The flange is secured by the porcelain tile and does not move. Can I install the toilet with the toilet flange not touching the floor?

The bottom edge of the flange should be even with the top of the floor. That would make the top edge of the flange about 1/4" above the floor surface. If I understand you correctly you are within 1/8" of perfect, install an oversized wax ring to be safe.

Is the top of the flange 1/8" above floor or the bottom of flange? A flange too high causes the toilet to sometimes not set flat on the floor and will rock