Trans women might not have periods. Trans men might have periods. Also, there are contraceptive pills able to stop periods completely and menopausal women doesn't have periods. If a woman has a hysterectomy, she won't have periods. People who are malnourished might lost their period.

So periods don't define womanhood. You can be a woman without a period. And can have a period without being a woman.

It is not about feelings, it is just factual. Deny a reality just because you don't like is absurd. At the end of the day, all those situations exist and denying sanitary products to a menstruating trans man would end with a bloody stain. Or saying that a woman is only a woman if she menstruates, begs the question, then what are all grandmas? Or women with hysterectomy? Did they suddenly become men? Something else? Again, it is absurd. XD