Like them or not, these SSPX folks really know how to make their point on solid doctrinal grounds.
There is nothing wrong with meeting occasionally in a Cathedral with people of other faiths. There is no pretense that this is a Mass or a replacement for the Mass.
That's exactly the rationale bishops all over the U.S. use when they invite radical pro-abortion "Catholics" into a church for some political grandstanding.
Abortion-enthusiast, apostate Catholics are the foulest of the foul; not to be compared with devout, morally upright, Torah-loving Jews. Observant Catholics have more in common morally with observant Jews than we do with, e.g. Andrew Cuomo or Nazi Pelosi.
I didn’t see anything about people being thrown out of the Cathedral for praying the rosary.
And I think there is a big difference between glorifying pro-abortion politicians—which I agree is wrong—and holding a joint prayer meeting with friendly people of different faiths.
I would, incidentally, draw the line at inviting Muslims to such a session, because I don’t think Islam is compatible with Christianity. But there is plenty in common among faithful Catholics, Protestants, and Jews. And what I used to say when I got together with Evangelicals is that we can agree to disagree on a number of points—but there is much that we hold in common. That makes it possible to work together, provided that you don’t push it too hard. I didn’t see any indication that that kind of false “ecumenism” was involved in this case.