This is what makes people cynical about empirical arguments in policy debate. Recognize when the data are inconclusive, or else no one will be able to recognize what counts as sound evidence.
If you are contributing to this devaluation of the currency of reason, just stop. In particular, stop insisting that everyone who disagrees with you on facts is either an "idiot" or a "liar."
Look: There are lots of good, thoughtful arguments to be made here, ones based on value and ones based on the best factual surmises we can make based on experience and sense.
These are arguments that citizens in a liberal society can advance openly, and should, to confirm, for themselves and for others, that their positions aren't motivated by the illiberal ambition to denigrate those whose cultural identities differ from their own. Reliance on one-sided, cherry-picked empirical arguments doesn't furnish that assurance; on the contrary, it's the "smoking gun" of cognitive illiberalism.