From a cost perspective, I'm not sure if feminine care products are more expensive than then additional calories men need on average – it depends on what you eat, I imagine. But suffice it to say, we shouldn't be too surprised that there is a gender-differential in spending needs, even beyond personal preference in what and how much to buy. There's a lot about life we can't choose, and sometimes that ends up with a gender differential.
Side Note: removing sales-tax exemptions across the board is probably a good idea, whether it has any adverse effects or not – many feminine care products do not get the same exemptions as analogous products for both men and women. This is also sometimes called the Pink Tax, but less commonly, and is really very easy to solve.
The claim that e.g. women's razors cost more, specifically as a way to bilk women, is very different. It's a strange claim. We all ought to have a (high-granularity) market efficiency assumption – that if someone was being bilked there ought to be a reason other companies aren't jumping in on the action. Plenty of people would be honored to bilk you at half the cost!
But more saliently, it doesn't match my experience as a customer. I've recently returned to using women's razors (despite being a man), because otherwise I have to be exceptionally careful or have a bloody, cut-up face after shaving. The extra few cents for a fancy razor is worth it for me, and the razors I had before weren't even men's razors, they were gender-neutral low-quality disposable razors. Spending more money on something with any branding at all is a luxury – one I'm happy to indulge in, but not a tax or discrimination in any way.
Which I think frames the discussion better anyway – it isn't as though women have to pay more – they could always buy the men's products anyway – but they're... encouraged to? Isn't everyone encouraged to spend more by modern branding?
No, they're being tricked – but wait, the prices are publicly listed. Then maybe they're facing societal pressures? But who watches them shave?
It must be price discrimination – that's no good to hear, considering I'm the only person on the planet who appears to care about price discrimination. Finally, my time has come! Except it isn't price discrimination, not really. The people can buy whatever they like, it's different products that have different prices. And that's a pretty essential part of the market economy.
As far as I can detect, the real problem is: many women want to buy an expensive way to reinforce their femininity. It's worth noting a symmetric claim could be made for men, and that there are some prisoner's dilemma forces at work on both sides here. You can avoid the archetype, but that makes you less legible and harder to locate as a partner. Loneliness is something we'd do almost anything to avoid, and what are a few dollars compared to that?
But this is just the same problem with social networks. People want to do something instead of something effective, like starting conversations, being kind or being generous. At the end of the day, the signalling value of effete signal-only expenses will turn negative. I'm optimistic that people will, in the fullness of time and wisdom, get their money's worth.