Is it legal to sale t-shirts with a beer logo which is back filled with a camouflaged pattern?

Probably not if the logo is a registered trademark of the beer company. However, if the intent is some sort of parody of the logo, you may have a free speech right to alter it.

The original beer logo is likely protected by the owner under both trademark law and copyright law. Your use of the original logo would be infringement - and you could be sued by the owner to (1) stop and (2) pay damages. Use a "made up" logo of your own. "BEER".

You should go to an attorney with the specific question so they can see what you are describing in the context of what logo and how it is changed. Generally speaking. if a changed logo is recognizable, there are likely to be problems, especially if the logo is owned by a large company.

It all depends on what the rest of the t shirt has on it and whether the use of the logo in any way would lead consumers to believe the t shirt came from or originated from that beer company. Also it must not disparage the beer company. The quality must be in line with the quality that the beer company uses for its t shirts. All in all it would be best for you to get permission from the beer company. However the reality of the matter is that if you are doing one off small production runs then the chances of the beer company trying to go after you is slim.