When you put it that way the similarities are stark but there is a fundamental difference
As it stands Bitcoin Cash is hanging on in there but has not even slightly dented Bitcoin or the enthusiasm surrounding it. If the whales were to create a fork from Bitcoin with a view to helping the community long term then Bitcoin Cash should have been pushed through with a clearer and stronger mandate with advanced attributes not possessed by Bitcoin. Just the desire to show the Bitcoin Board (as you put it) that they could fork and create a new coin was never going to be enough. It seems the Bitcoin Cash creators always had an ulterior motive which was to reap financial benefits that fork would bring but would never part with their Bitcoin regardless. If they really believed in Bitcoin Cash those whales would have got rid of the Bitcoin and that is the fundamental difference between the two scenarios because both those Christian denominations followed their own religious edicts after the split without weaving in and out of each others' teachings and without holding on to the cloth of the other group just in case they needed jump ship and follow the other group.
In this case people who gained Bitcoin Cash as a result of the fork should sell all their Bitcoin and hold their Bitcoin Cash till their hearts content, that is if they actually believe in what they preach. Those holding Bitcoin who did not want the fork but received Bitcoin Cash should by all means sell them and follow the yellow brick road to Oz via Bitcoin.
If I may add, those Lutherans was just confined around Germany, Austria (if my memory serves me right) and didn't gain enough traction from the Catholic community, maybe they swayed a few but Catholics remain the dominant religious group throughout centuries and Lutherans didn't took off as expected.
Similar to what we are seeing today, after the split there was an attempt by BCH fanboys to overthrow Bitcoin, with negative attacks and spamming the bitcoin network, but they didn't succeed. Community knows better who are behind Bitcoin Cash, all greedy individuals who are trying to portray Bitcoin Cash as the new Bitcoin, but what happened? no support from our community. Just like what we have witnessed during the religious schism in the 15th-16th century.
Right, the Lutheran split was an ideological one, I'm not sure they were ever concerned with overtaking Catholicism so much as maintaining a pure ideology and abolishing what they viewed as corrupt practices the Catholic church had adopted (especially the selling of indulgences). Lutheranism may have started in Germany and Austria, but it has a pretty largish following in the US (at least judged by the not insignificant number of Lutheran Churches I see all the time, albeit this is anecdotal). I'd say Lutheranism has become a major subset of the Christian religion, with a congregation numbering over 80 million worldwide. As for the BCH folks, I can't say whether they're ideologically pure or had an ulterior motive that was based entirely on financial gain, or a combination of the two somewhere in the middle. I just find the cultism on both sides to be pretty striking and analogous to historical precedent. The difference here is that BCH does view BTC as an existential threat, and if BCH ever became large enough BTC would view it as one as well I'm sure. And because both sides view it as a zero sum game, both must demonize the other side and battle over the hearts and minds of crypto users.