Running wider tires in the front I currently run a full suspension bike with rather thick tires. I have however been thinking of changing the rear tire to something a bit thinner as the current tire I run makes the wheel very close to the linkage and frame. When there's even a bit of mud, the mud tends to stick to the wheel and the frame causing the rear wheel to completely jam. Is this a good idea or not recommended?

It is common to run different sizes front and rear however your tire should never jam into the suspension. It seem like a larger diameter wheel has been installed. Like a 27.5 wheel into an older 26” frame. Could be dangerous if that occurred at the wrong time!