Perhaps my greatest gripe with the Latin Mass world is that in about half of TLM Churches I've attended, this woman would be viewed with extreme suspicion -- because much of the TLM world has a basically petit-bourgeois culture of "keeping up appearances."
I have noticed that even if I wear a nice suit jacket, comb my beard, wear a decent pair of boots, and so on, many of the Parishioners at the various TLM's I've been to are leery of me. They ask what I do for work, and my answer makes them fret. Or, in the event they're familiar with my writings (or my past), a sizable portion of TLM-goers have already formed an opinion about me before we have even met.
There are Churches that I simply have no interest in visiting now because there is such an intense "mold," and I do not fit it. Many of these Churches quite literally watch the door, they do not advertise their Mass schedule, there is an air of paranoia; you can feel the nervous energy pervading the place. The vibe is not welcoming, it is one of "who are you and why are you here?" One gets the sense that they have overcorrected against the ills of modernism and the secular world. (this is one reason of many I won't generally attend SSPX, for the record; they are particularly bad about this)
Contrast this with the local Novus Ordo, the Franciscan Parish, or the Byzantines -- they are most often simply happy to see a new face. There are TLM's like this, to be sure, but they are in the minority.
I'll always defend the preconciliar Liturgy, but I have no defense of this unspoken idea that we should return to preconciliar levels of social conformism and "keeping up appearances."
This is one very good thing about the post-Vatican-II Church, at least in theory: the openness to all mankind, regardless of their history or manner of living... We welcome them first, guide them away from sin and towards God, and have no real interest in enforcing total cultural, social, or behavioral conformity outside the bounds of what the Catechism teaches.
Liturgically, I want the reverence and the tradition of the old Mass -- socially, I want the openness and warm fraternal spirit that Vatican II promulgated. This is very rare...
Would this woman be welcomed in your church?