Harem in itself is not bad, but its introduction tends to apply a negative modifier to likeability for me, as they tend to detract from just about anything else more interesting and/or 'here is the protagonist with all the love interests after them, please relate yourself to the protagonist'. Obviously I'm not the demographic being pandered to.
Mm... me, it's
romance that is the baseline negative modifier more than what form it takes. I actually kinda' enjoy well constructed romance plots, but by default I'm notably more leery of a piece of media that includes it than one that doesn't. Tends to lead to really lazy character interactions or
incredibly unhealthy relationships, even outside of anime. That said, it's a
lot easier to initially hook me with an attempt at polyamory than it is with something more mundane. S'more exotic, y'know? Frumple likes the OT3+.
Even most harem setups in anime tend to functionally be monogamous with jealousy gags and fanservice thrown in, though. It's unfortunate. I mean, I generally like the fanservice but I could do without the jealousy, heh.
... actually, can anyone think of an anime that's full-on polyamorous? Not polygamic or polyandric, but something with more than one of
both genders. Stuff's freaking rare period, not just in anime. Usually you get threesomes or one side going solo at best...