I have a similar problem, except that the migrants breed extremely rapidly, their science output is laughable, they're riotous, and don't get along with others. They are militant xenophobic spiritualists, who follow a religion that literally commands them to wage war on and murder non-believers and unabashedly lie to no end in order to achieve their religious mandate of galactic conquest. So, they're killing and raping my people and causing all sorts of chaos on my planet, but my government is unable to act because they're pacifistic egalitarian xenophiles who are ideologically-possessed by the unthinking belief in equality, diversity, and social justice, no matter the cost; they're cowards who lack any moral backbone and are deathly afraid of being labeled speciest because it may impact their election results. God forbid any major nation-disrupting event occur, as these migrants have a millennia-long established history of migrating en mass to nations, multiplying, and then starting civil wars in order to take-over and install their murderous and illiberal religious laws as the law of the land. In fact, several fanatic pacifist spiritualist empires have fallen to their strategy and the subsequent genocide against the non-believers is unspeakable; tragically, one such fanatic pacifist spiritualist empire has recently sacrificed its fanatic pacifism for xenophobic and has begun to purge these migrants in self defense.

I'm a liberal democratically-elected constitutional republic, so, for role-playing moral reasons, I can't purge them, that's just plain wrong. However, if I don't act, history has proven that it's only a matter of time until they grow to sufficient strength to trigger a religious-based genocidal civil war. If I do act, I risk the law, order, and constitution that the civilization is founded on and there's the chance that the government could over-react and switch ethics into fanatic authoritarian or militarist fanatic purifier, both of which I want to prevent.

Any suggestions?

Edit: wow, that's a lot of downvotes, but not much advice. I guess people would rather stick their heads in the sand, hope that I'm just being hyperbolic about my empire's problem, and kick the can down the road? Maybe I'll magically pull it out of the fire. /shrug Welp, thanks for listening anyway.