2nd and 6th (ie B and bottom E) makes it pretty much a cert that the issue is end compensation. A vibrating string in its simplest form forms a sine wave between two fixed points. Then you add overtones, ie multiples of the same sine wave. The fixed points are called "nodes".

A real string as opposed to a theoretical one has both thickness and stiffness. So it behaves as if the nodes are a little bit in from where the fixed points are (the nut or fret at one end and the bridge at the other). The thicker and stiffer the string, the further in. So the thickest and stiffest unwound string, the B, suffers more than the top E and likewise the bottom E.

THat is why all guitars now have saddles that make the top E string a smidgeon shorter than the bottom E. Many also have the saddle shaped so that the top E contacts at the front of the saddle but the B at the back, the G at the front and the bottom E at the back with the D and A in between, proportionately. Felten nuts do something slightly similar at the nut end.

Taks seem usually to be built with a split bridge that assumes you are going to play an un-wound G, and with a HUGE additional compensation, and I find they are often a bit iffy about capoing for that reason.

The lower the tension, the more effect the pull of a capo has on pitch, so choosing a set of strings that are right for the tuning you play makes quite a difference too. I play one song with the bottom E down to A and fretting that string without pulling it sharp is challenging.

Another factor may be that if you palm mute, you also tend to move the saddle node up the string.