I wonder if I'm able to use alternate costumes for the Bat-Fam in the main story (Not NG+)

My argument for why they should be allowed is that they have no advantages other than looking cool

Using DLC skins is allowed in all categories. In general anything you can do within the game itself is fair game unless the leaderboard rules explicitly say otherwise.

Note that modded skins are not allowed, though.

Thanks so much. I've been practicing for a main game run but I have a favorite DLC skin to use for batman. I like the Batman Beyond skin for him.