The party was originally found in the 1870s and a Catholic party in Germany, then dissolved when the Nazis came into power and Hitler took control, then was refounded, but could not rise again to its former importance. Ultimately, however, its always been a Catholic party, even if that's absurd.
Given the more common name for this party is the Catholic Centre Party it seems fitting that it is a party intended for only Catholics. In reality I assume it doesn't matter because the party is so marginal that it really doesn't matter. But overall it depends on the parties strategy and who they want to join.
Many of the values supported by the Centre Party could apply to all kinds of different people so there's no reason why membership should be limited to Catholics.Although Catholics started the party they could definitely benefit from joining with other denominations to create a mutually beneficial political coalition for various faiths.
No, I do not think that only Catholics should be members of the Centre Party of Germany, because I think that there are better political parties in Germany for all people, not just Catholics, to be a part of. The Centre Party of Germany had some controversial positions during World War II, and they remain a controversial party.
Germany's Centre Party can come back, but it has to be more inclusive than just have a basis on Catholic ideals. Germany and Germans can have a strong party once again if the Merkel administration fails. Unfortunately, it will take a massive shake-up for the Centre Party to be relevant again.