There's no certainty that Lawgiver == Bane
Bluebomber (whom his kinda the highest authority around regarding the in-game lore on the server), commented as follow in several different threads.
That's not very relevant. This forum section is about Ravenloft specifically, not PoTM.
Therefore, every Banites/Lawgiver followers should acknowledge that they are one and the same god.
No, that's not really plausible. There's no certainty whatsoever given to FR Banites that Ravenloft Lawgiver was their god. They may, though, believe so.
[...] Native worshippers don't know him as Bane, they know him as The Lawgiver. It is said any who heard his true name would be struck dead. Only those really in the know of how the dimension works probably know him as "Bane". [...]
That's actually not accurate. As I said earlier, the publishers of the 3rd edition books couldn't use the name Bane. In all 2nd edition Ravenloft books he's referred to by the name of Bane. As we are not bound by the legal/licensing issues that Arthaus was, I see no reason not to call him Bane.
So, no, there should be no questions whatsoever that Bane and the Lawgiver are one and the same.
I know the history behind the name and behind the Lawgiver's church's history, but when I say that it's not necessarily true that Lawgiver is the very same as Bane, I mean that it's not known (and that's made quite clear in the sourcebooks) whether it is Bane who gives the Divine powers to the followers of Lawgiver in Ravenloft.
Whether it was decided that on this particular server they are the same gods in current day Ravenloft, does not mean that the PCs were aware of such a decision-- They would not, and it'd be up their character alone to believe one way or the other. It's very much supposed to be that way -- Unknown. And because of the certain largish differences of the churches, I'd find it hard for majority of FR Banites to accept the church of the Lawgiver. They're both very strong about their believes and don't accept deviations easily.
This is, of course, not to say that it was
impossible for a FR Banite to turn to the church of the Lawgiver or that it wasn't a source of good RP. It certainly can be!
EDIT, addentum: I think FR Bane's church and Ravenloft Bane's/Lawgiver's church are quite good showcases of how faiths may grow to have distinct differences over time. In a way, Lawgiver's church is much milder in its stances and does not as fiercely oppose almost everyone.
Similar changes could happen to say, a follower of Torm. He may grow less absolute in the Domains of Dread -- Though equally much the opposite could happen. After all, if you smite just to be sure, you'll rarely let evil escape. Gods will take care of the few innocents that go with them!