I can understand not wanting to turn down a visitor but why not have an after hours tour? Why submit all the children and the families to the confusion and the pomp and circuмstance for someone who a) may not even be a proper bishop and b) is a hardened liberal whose company would have been forbidden in saner times?
The SSPX leaders think that if they play the game these men will convert.
(or
maybe more properly, "revert". God only knows which it truly is.)
I suppose if they had had an after hours tour they'd be criticized too as if they were trying to keep it secret. So maybe they can't win. But I am okay with that. I don't think they should in this case. Leave the NO to itself, people leave it for a reason.