Isn't an SSPX chapel a Roman Catholic chapel? In a Roman Catholic church, isn't everyone welcome? Hasn't that always been the case? Why, just because someone disagrees with +Fellay and vocalizes that disagreement, should they be barred from the church building? Isn't the Roman Catholic church for sinners?
If I were a Jєω, protestant or muslim, I could come in and attend Mass. I couldn't receive the blessed sacrament, but I would be most welcome to be there. My point is that the Holy Mother Church doesn't refuse entry to anyone.
Now, there may be a crazy person who interrupts the Mass, causes disturbances during the Mass, etc. There are legal remedies for that. The priest can get a restraining order against that person, but the priest must show that the person is causing a disturbance.
So, unless there is a restraining order, who can stop anyone from attending an SSPX chapel?
The question becomes a basic question. Is the SSPX Roman Catholic or not? If they are, then they can't refuse entry to any sinner and more importantly, they should not.