It depends largely what "socially conservative" means. Adopting a "I don't give a fuck" attitude towards other people's personal identity and just letting people live their lives is probably fine. Actively being homophobic or racist in order to seem more appealing to homophobes and racists only results in the party being taken over by them and abandoning any socialist principles.

(Edit: Not trying to call you out or accuse you of anything here, sorry if it came across that way, that's not my intent at all.)