First, the premise is false. Greeks and Romans were not at all "white" by modern standards. Not only was skin color not a social construct at the time, but most Mediterranean peoples had darker, bronzed tones. And yes, slavery & patriarchy have existed in every single society since the dawn of time, until very recently. Just because the affordable care act didn't exist in 1991 doesn't mean I will refuse to use Linux because it was created in a time without basic healthcare rights.
The real reason for the decline of classical studies (and more generally history) is because corporations are offering graduates with STEM degrees higher salaries.
I don't think this is a good trend either. I've personally gained more from self-studying the classics than anything from my CS degree.