A simple Google search turns up conflicting answers. One source says that some temples have no restrictions on menstruating Mormons, require menstruating Mormons to wear tampons, or bar menstruating women from being baptized. Do these restrictions really apply to new converts? Do they vary within individual Mormon temples? What about churches? In individual churches, are Mormon converts who are menstruating on the day of the scheduled baptism barred from baptism, or do they have to pick a different day? Do menstruating Mormons have to wear a tampon? Would a pad suffice?
There is no "official" statement that I know of regarding this. The Church does not consider those who are menstruating to be unclean. There is no rule against being baptized during that time.
Temples provide tampons for the women who are. As long as they are using one, there isn't a problem. I read what you were referring to from the link you posted. That was the opinion of the temple worker.
In regards to the convert baptisms, I don't know of anything either way. When a woman is baptized they are not asked if they are menstruating, so there is no way to know unless the officiator is told.
Edit The Church Handbook of Instructions contains nothing concerning this matter. So it is safe to say there is not a big deal. If it was, the handbook would state it.
How does one post a reference to the absence of a policy? There is nothing in the manual, so nothing short of publishing the manual in its entirety would suffice? Having baptised women, and being around many others who were baptised, the question has never come up. Full stop.
Has some individual gone off the rails and started asking questions they shouldn't? With 15 million people, a lot of crazy things that aren't sanctioned or doctrine have, on occasion, happened. That just means there was a nut job that is doing their own thing, not that it is policy or doctrine. Anyone who is a life-long member should be able to answer that one with conviction.
Menstration does not preclude a woman from baptism, as the topic is never broached in any official (or sanctioned unofficial) capacity before or at the time of baptism.