I use Axe and I love it (I know everybody else seems to hate it though)
I tend to sweat a lot, so I feel safer with it and find that I don't smell like sweat with it. It's pretty strong. I'm pre T but my sweat odor is strong so I need to feel safe and clean. Plus, I just love its smell.
Or I just use gender neutral deodorants.
It's just marketing. Fragrances change, men's fragrances are stronger. Nothing will happen to your body though, don't worry. I also use men's shampoo because I like the fragrance, and my hair is fine!
So yes, in cases like these (deodorants, shampoos....) it's just a marketing strategy, and a matter of fragrance preference.
Gendered toothpaste? This is ridiculous! I hate this b.s. I can't believe people would buy a gendered toothpaste. I wouldn't. The reason why I buy men's shampoos and deodorants is because of fragrances. I don't like feminine fragrances, they smell too soft and sweet for my tastes. And I wouldn't want to "smell like a woman", in the sense that it'd just make me feel uncomfortable and more dysphoric. I also use men's razors to shave my armpits in the summer.
I speak from personal experience, I'm pre-everything, I've been using men's products forever and my skin and hair are fine, lol. It's just marketing nonsense.