Variation of compressiblity factor with temperature
Remember the mathematical definition of $Z$:

$$ Z = \frac{pV}{nRT}$$

Given all the $Z$ graphs I've ever seen -- the single-point interaction of all these isotherms is just coincidence (and kind of misleading). There is nothing in thermodynamics that suggests for a given gas, there exists a $p$ for which $Z$ is constant, regardless of temperature. Even for constant $V$ and $n$, you have that $Z \propto \frac{p}{T}$, so changing $T$ can in no way leave $Z$ constant.

You can find graphs that look similar even for different gases at the same $T$:



Nonetheless, there is no reason for a given material to have the same $Z$ at a given $p$ regardless of temperature:



Generally speaking, if you zoom-out far enough, and have significantly different temperatures (like 100s of Kelvin apart), some $Z$ graphs may appear to have a uniform $(p,Z)$ point, but in reality the intersections are not uniform for any physical/mathematical reason. For this reason, graphs like that can be a little misleading.