Conversant imo isn't the right word. JKR has a wide knowledge of the mythological stories, but only as stories. She completely misses the spiritual meaning those stories have to believers of the various faiths. E.g. the 'white doe' to a Celtic-based Pagan is a sacred symbol of a mother goddess or her personal messenger. Its use as Snape patronus is acceptable, but to equate it to Lily Evans can be seen as offensive. It made me feel the same as Mary felt about the monument at Godric's Hollow, just a bit too much.
I hope that JKR didn't realize that she might hurt the religious feelings of some readers, but after the last few interviews I fear she doesn't care.