I believe that period products should probably be free, but I think there's a false equivalency between them and condoms, and I also question whether it is part of a war on women.
Condoms are free because if they weren't, a large proportion of those people who use them would be significantly less likely to use them . This would lead to increased pregnancies, increased abortions, increased births, and increased disease transmission, costing the government more money than providing free condoms in the first place would have done. The state not providing free menstrual products would have a less damaging effect on it's long term budget, in fact, I would question whether spending money on period products would save the government any money at all in the long term, as spending on condoms would. The provision of free menstrual products is an end in itself, rather than a means to an end, which the provision of condoms is.
In this way, I don't believe a comparison between condoms and menstrual products is a particularly useful comparison, I think a better comparison would be between menstrual products and medicine, or menstrual products and the flu jab, or menstrual products and dental care. The state charge for a number of necessary products, from prescription charges to flu jabs to dentists, these costs can depend on the council, or part of the country you live in, the non provision of period products is part of a broader picture, rather than part of the systematic oppression of women, which does of course exist and is a problem on a global scale.
I would also add that not just women get periods, and that both non binary people, and men, are also able to get periods. The framing of period products as a women's issue can do a great deal of damage to our trans brethren, and I think we need to keep in mind the problems of trans erasure in our rhetoric.