I can understand the reluctance of nonCatholics to use the English word "church" to identify themselves. In general, Jews despise that charade as duplicitous and dishonest. Jewish Community Centers, on the other hand, are actual assemblies of Jews and Gentiles without that deception.
It would be better for Christians to use the Biblical word of ECCLESIA, to avoid the confusion with the word “church” ... which is not used to describe Christians.
One could say that I am a member of the ECCLESIA of the New Testament, and I happen to go to a “building” that is called a church in secular terms, and that this building was built or is occupied by an “organization” ... neither of which (”church” or “organization”) has anything to do with being a member of the ECCLESIA.