"MLCC" is a description of the internal construction (multi-layer ceramic capacitor), not the dielectric.
They are available in "good" dielectrics (C0G), mediocre dielectrics (X7R), and crummy dielectrics (Z5U) (ranked for use in resonant circuits), among others.
C0G capacitors are available in lower capacitance values than the others, but nowadays 0603 C0G 10 nF capacitors are available (more expensive than X7R).
C0G/NP0 has excellent temperature stability (+/- 30 ppm/K) and excellent loss (high Q).
Plastic films have lower temperature rating than ceramics, important for SMT soldering.
Polypropylene film capacitors are excellent, with very low loss, but somewhat worse temperature co-efficient (-250 ppm/K), usually TH (leaded), and harder to find in low capacitance values like 100 pF.
PPS (polyphenylene sulfide) film is available in surface mount, and has similar quality to C0G ceramic, but is only available in larger capacitance and case sizes, since otherwise one would use C0G.
Kyocera PPS capacitors start at 1000 pF and 1206 case size.
Tight-tolerance capacitors are available, but naturally they are expensive.
If you have a way to measure frequency, you can use two capacitors in parallel: measure the frequency with only a larger one in place (for a higher frequency), then add a smaller one to reduce the frequency.
The tolerances quoted in the catalogs are the range of capacitance that comes out of the production line: temperature drift and voltage-induced changes (for crummy dielectrics) are over and above that tolerance.