Old post but this discussion is a bit personal for me because I was convinced for years that it was
I played DMC for years, then once I converted, I left Devil May Cry for what I thought would be forever, but two years later, I did a study, and it turns out the angels and demons in the DMC world are absolutely nothing like how they actually are. The Japanese have always had a weird perception of how angels and demons actually work. Quite unrealistic. I will say there are parts of the franchise I really don't like, but I play for the gameplay and nothing else, so I don't let it concern me much.
There's a Catholic saint who's named Lucifer, so don't get too hung up on names. The Japanese are just edgy to dorky degrees. Christianity does exist in the Devil May Cry universe, but it's never insulted.