Always runs
I think throwing her out on ****** is not the answer. If someone does something unusual or against our beliefs, I think it is incumbent upon us to ask them about it and to clarify that the shul is a very traditional one where specific roles and customs are adhered to and to please abide by them or locate a “synagogue” that permits veering from mainstream thought (that her presence is welcome in the context of keeping with the Shuls beliefs and customs). Throwing a person out, ke-ilu in anger, should rarely be an option, except where a discussion has already been had and still the person chooses publicly to ignore requests.
Wasn’t bar-kamtza thrown out in anger despite his begging to be allowed to remain to avoid embarrassment (and see what that brought)?