Mary Magdalene's Synagogue ???

Here is a report about the discovery of a Jewish synagogue from the time of Jesus Christ:

https://www.jpost.com/archaeology/2nd-temple-period-synagogue-found-where-gospels-mary-magdalene-was-born-688519

Here is what one expert had to say:

"We can imagine Mary Magdalene and her family coming to the synagogue here, along with other residents of Migdal, to participate in religious and communal events," Avshalom-Gorni further said.

I think IMAGINE is definitely the right word to use, especially in light of the exclusion of women from much of what happened in the synagogues of the time:

https://lifeofthesynagogue.library.cofc.edu/section-7-women-in-the-synagogue/

Additionally, it's often claimed that Mary was a known prostitute. Would the rabbis of the day even let her come near a synagogue? I suspect not. I don't get the impression they were a forgiving sort.