What is the current through a parallel LC tank circuit in its resonant frequency?
Firstly, series resonance and parallel resonance are very similar in frequency but they are different. So, at series resonance the impedances of Lm and Cm precisely cancel leaving Rs (or Rm as shown below) as the dominant impedance. Rs happens to be in parallel with the shunt capacitance (Cp) but, Rs dominates as it is quite low (circa 100 ohms).
In parallel resonance (a slightly higher frequency) the series inductive reactance is slightly higher than the series capacitive reactance and this means that the resulting net inductive reactance becomes parallel resonant with the parallel capacitance (Cp).
Here's a better view of things: -

I've put some numbers on things to show typical values for a 10 MHz crystal. The above picture taken from my answer here.

What I only know is that impedance is max at parallel resonance but I
don't know why the max impedance in this configuration is equal to the
load cap

It isn't and you are right to be confused. There is a lot of BS written about crystals from some sources that should know a lot better.

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