Exile used to be a tempting idea to me too, but it’s a bit of an “out of sight out of mind” solution. The exiled will end up somewhere, and likely damage the environment and original inhabitants of the area. Just like the first colonialists destroyed the food sources of Sydney’s Aboriginal population in the late 1700’s (and that’s before we get to the possibly-intentional spreading of smallpox).
Even if we could ethically-ish dump them on the moon, you’d just be creating a hostile neighbour. Sci fi has already well and truly explored the possible outcomes of that scenario for us.
Unfortunately, we as a society made them, we’ve got to be the ones who contain and prevent the damage they cause. And somehow, we need to do it ethically too.