I suppose you are welcome to whatever you choose to believe, and in order to believe it it must seem true to you. For what it's worth though, I draw the line at being held guilty for the sins of my fathers, or anybody else's fathers for that matter.
I don't know you well enough to say, Nick, but I would hazard a guess that if what you say about "bad group-karma" is true, then surely there is at least one group and probably several groups to which you can be included by extension (the same kind of extension you are offering Thomas). Which would reduce the argument to the pot calling the kettle black...
I certainly wouldn't of my own volition accuse you of being guilty of trying to subvert and politically wrangle all of the world faiths into one corral, for who knows what nefarious purpose...just because I had that conversation with another Theosophist. Of course, when I called the bluff there was considerable backtracking and attempting to deny...but the evidence was there in his own words. According to your very own standards you are eliciting here, you would be guilty of the same conspiratorial conniving, by virtue of "bad group-karma."
I know how it can fuel an ego to get a representative of a self-referential institution that claims infallibility to admit fallibility...but going so far as to accuse that representative of having a murderous heart and intent against those who disagree with him, is just wrong. Otherwise, the same could be said of any Theosophist for precisely the same...the desire to murder those who will not willingly fall into the fold!
I am making no excuses for any church...I have no need to. I am beholding to none, but G-d alone. Different periods of history brought different human tragedies brought about by differing understandings and differing culture clashes. No culture I can think of is immune...though some are more visibly evident to us in part because of the Western cultural lens and disposition we are viewing from. Even the uber-pacifist Buddhists are not immune, historically. Even the Native Americans waged war among themselves. The East Indians still wage cultural and psychological war of self-denial to distance themselves from their Aryan ancestors, and the Chinese-Japanese-Korean "who came first" and "who has the biggest/baddest/bestest" penis envy continues today after thousands of years. So you caught the Catholic church in an OOOPS. Not to make light but, big deal...there are plenty of OOOPs to go around. Humans are prone to OOOPS.
In my humble opinion, to seek the betterment of humanity includes being able to look beyond the OOOPS. The only caveat I can see is unless that OOOPS is current and ongoing and you happen to be caught up in it or are in a position to do anything about it. If there were a Catholic Inquisition going on today, yes I could see taking a strong stance against such. But there isn't, and there hasn't, and accusing someone today of injustices waged hundreds of years ago is simply not justifiable in any real sense.
Unless one happens to be trying to validate their own injustices?