Weird thud sound when plucking

As a few people have mentioned, you are probably using a rest stroke - meaning your finger plucks the A string and then hits the E string, causing a low frequency thump. If you don't like that sound (it's a thing, but not necessarily a bad thing), you can land your finger on your thumb as you mentioned (I use that technique sometimes). Or you can use a free stroke, where the finger travels over the E string after plucking the A string.

I used to play exclusively with rest strokes, as that gives the biggest and most muscular sound and a bit of free muting. But free stroke is nice for getting more delicate and singing tones.
 
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This is my thought as well. I forgot to add that the sound is particularly prominent on the A string. The only way I can get rid of the sound is if my middle finger hits my thumb instead of E string. I have tried different hand positions.
The thud is your plucking finger hitting the E string. Two things that will help. One lighten up on bass on your EQ, and add more low mids. Second is a lighter touch when plucking. A side bard to that is strings will last longer.