Input loading on a standard 100mhz chinese probe is 16 to 20pF.
That’s around the size of the pair of caps on the crystal and the
clock driver is pretty robust. I looked at an atmega324p with
a 20mhz crystal using a crap 10X probe and got a perfectly good
sine wave on both XTAL1/XTAL2 pins. A FET probe is overkill
for this application.
Note that there is a "low power/full swing" clock option on the
clock driver. Using the "low power" setting may not drive the
crystal hard enough to tolerate the probe load and will cause
other problems in the real (noisy) world.