The CPU you quote supports AVX, including AVX2, so no that is definitely not your issue.
AVX refers to several families of newer instructions to optimize certain kinds of arithmetic by running multiple operations in parallel on wider data registers. Some software requires newer CPUs requiring them and will crash instantly if run on an older CPU. Other software uses the faster instructions only when available for certain optimized tasks.
There should be no difference other than the speed of data calculations between a CPU with AVX and a CPU without AVX, or supporting only older versions of the AVX instructions. When MSFS came out in 2020 I tried it on an old 2009 Xeon E5520 which didn’t have AVX at all; everything worked fine but it was much too slow and I had to upgrade my old CPU to get acceptable performance.
I doubt that if you’re having a problem with enabling avionics that it’s related to AVX: for one thing you have AVX, and for another it’s unlikely for such a problem to exist unless there’s a very weird bug in the non-AVX code path.