100% ABSOLUTELY the quality thing. I was a cofounder of a group once that regularly turned down art for being low quality. I get not accepting unrelated things, screencaps, demotivational posters, edits, or even manga colors, but the last thing you want to do is offend any members.
And although no group manager should participate in a ship war, some groups are made specifically for a certain ship, and managers in this case ABSOLUTELY have the right to defend their ship ~in a professional manner~ without bashing another. If a member joins to troll and the manager gets huffy, I don't blame them. It takes a lot of effort to run a group. (I'm the founder of a shipping group, and although I go out of my way to make everyone feel welcome and am a multishipper myself, it really gets on my nerves when you get someone who's like "HAH I HATE YOUR SHIP." It just kind of spits on all the hard work you've done.) So that's why I didn't vote for ship wars~ because some groups are specifically a safe haven made ENTIRELY FOR an certain ship, and promoting other ships would actually be going against the premise under which the group was made. (Although I completely agree that although the owner can be biased, they should be respectful still and not openly bash another ship or its shippers.)