Personally I think either he, or his wife, or both, doen't trust Pence to conduct himself appropriately in one on one meetings, in which case I'd have to wonder why that would be the case, or if it is as he claims, that it's for religious reasons, and if they're interfering with his job, then maybe he should have a different job. It makes no sense to hire a butcher who's religious beliefs precludes him from handling animal meat. This is the same principle. If your religious beliefs preclude you as a politician from one on one meetings then either find a new job, or work out a solution. Conflicting religious belief is not a reason to not do your job.
In my profession (teaching of minors), it is best practice to never be in with a student alone in a room. This is not because the teacher (me) is prone to misconduct with that student or that things could easily slip into that. It is purely for safety and legal reasons - even if nothing ever would happen. There never can be misconceptions or false accusations with other witnesses in the room with us.
I am an itinerant teacher (meaning, I pull students out of their classes to work with them). Sometimes they are in groups, but sometimes, especially in absences, the result ends up being 1 on 1. It does not mean that if the situation results in this, that student does not get serviced. It just means that accommodations need to be arranged so that student still gets serviced in a way that we don’t violate the practice of not being alone in the room with that student. Usually that means an aide would join us or we would do it outside where others are present, etc.
I think the difference in opinion here between those that agree and disagree with Kamala is that when Pence says he won’t dine alone with another woman, the Kamala supporters automatically read this as = Pence not doing his job, whereas I, based on my experience above, do not necessarily see it as equal that. It just means that, when he needs to do his job, and his job requires he meet with a woman, then a little bit extra is needed to make it happen is all.
Pence probably indeed has a subordinate join him on all these meetings or just does it in a more open area. Heck, maybe the security detail that is around him all the time already satisfies him in this regard. After all, we are talking about a quote made 16 years ago.