Yes, these kind of movements do hurt electorally. The sentiment of them, for those who care to actually listen, is not that off-base though. It's just that straight cis white men are often incapable of humbling themselves enough to see that it's possible they just might occasionally play into a regrettable culture that puts Others down. They put up such big blinders because, frankly, they're the most emotionally insecure voting block in the country.
I guess Obama was one of the few politicians who could get away with upholding the truth of all this without bruising the fragility of this key group. Being a man was a huge plus. And sadly it'll probably take another man to pull it off.
It's not the hashtags themselves that are hurting the Democratic Party. It's the sentiment behind them that is hurting the Democratic Party. The type of sentiment expressed in the quoted comment above. This is very representative of mainstream Democratic officialdom. Why on Earth would a white person want to vote for a party whose leaders believe this?