As Goffik has said, everybody’s anatomy is different.
I play quite a few things that involve using my thumb on the low E, but I can’t remember the last time I had to play a thumb over G.
Things like muting when playing an A, you only need to touch the string, but I suspect the issue is you need change how you fret the other strings.
As a beginner you’re taught to keep your thumb on the back of the neck to avoid ‘sloppy’ technique, but as you develop as a player, you’ll learn lots of playing actually involves pretty ‘sloppy’ holding of the neck. However you’ll also learn where and when you need to use ‘good’ technique.
I suspect your main problem is you need to learn how to fret the A using a more ‘sloppy’ hand position with your palm touching the neck. Ignore trying to mute the low E, and work on fretting the A with your palm against the neck. Just like originally learning chords, it’ll be using bits of your fingertips without callouses, so it’ll be difficult at first due to the string sinking into your finger, but it’ll get easier with practise.