Conflict isn't ours to prevent.
Because millions of lives lost means nothing to you?
We should protect our citizens, not other countries' citizens.
What is so special about our citizens as apposed to that of our allies?
We will not allow the refugees in.
So we should let the die?
Public image would only be bad if we let it. If necessary, make laws that bleedinghearts can't speak ill of an America that's only protecting them and theirs. If you still feel bad about it, let people donate charity money to the refugee camps along our borders, individually. Don't force it on the taxpayer.
That won't have any effect on anti american propeganda, if we allow this to happen to one of our allies, why would any of them trust us?