As a woman who was single and dating, saying you don't have a social media is a red flag. Best case scenario, you truly don't and it's probably from having some sort of arrogant judgement value about people who do, worst case, you have a spouce you are hiding from me.
Either way, not worth the risk. Like all the women I know feel the same. Sure it's a historically newer redflag that didn't exist 10-50 years ago, but neither was worrying about crypto gambling and manospehre BS. Modern problems require modern precautions.