I noticed something:
I had my tabs in this order: [default], [Added], [Completed], [Abandoned] and others.
When I installed the new beta (11.1 beta 1610), the order of the first two tabs changed to [Added], [default], while the rest stayed the same. From what I understand, the [default] tab is unmovable (at least for me, it can't be moved), and now the [Added] tab also became unmovable since it ended up before the [default] tab.
So, I created a new tab and moved all the games from the [Added] tab there, then deleted [Added]. Now all tabs are movable again—except, of course, [default].
So, I assume that if tabs end up before the [default] tab, they also become unmovable.