The same system without the four initial conditions takes barely any time.
It has nothing to do with IC. It is FullSimplify which takes very long time. Try
Timing[DSolveValue[{OdeM, OdeP, Ic1, Ic2, Ic3, Ic4}, {V1[x], V2[x]},
x]]
On my PC, V 13.2.1 it takes 4.5 seconds
ps. I renamed your σX^2 to $w$. As I mentioned in your other question wrong-sign-in-variation-of-parameters-method , it is bad idea to use two letters for one variable. Why do you insist in using σX for a variable instead of say w or any other single letter?
Any way, it is well known that FullSimplify can slow things alot as it tried many types of simplifications. Try to use it only if needed.