It should be possible to remove tags (don't return items with this tag) from the results of "Browse".

It's possible, as explained in this old topic, and discussed in countless others since, including the one pinned at the top of this category.

It lacks "stickiness." If you switch from "popular" to "top rated", you lose the ?exclude=.... part of the URL. A second row of tags labeled with "exclude these tags" (and adding "include these tags" on the exist row) would help. Also if the backed handled it, the "sort by" links should would then include the ?exclude=... part of the URL when you clicked them. (And they would be listed in the left as excluded.)