555 Schmitt Trigger works well with CMOS LMC but not NE555?
Do you have in place the 10 nF input coupling capacitor? Perhaps what is going on here is an input impedance effect.

If we consider the comparator inputs on the 555 to be basically like open-loop op-amps, that means that their input impedance depends on the device used (CMOS versus BJT). Negative feedback isn't there to help with impedance.

The CMOS inputs will have a high input impedance and so the input of your circuit is basically dominated by the two 100K biasing resistors, which create an impedance of 50K.  In combination with the 10 nF coupler, the input passes through everything above around 300 Hz. (The -3dB corner frequency is 318 Hz).  This is well below the input signal frequency.

But what if the input impedance is somehow seriously degraded with the NE555?

Just a thought.