I agree with the linked article that taking cross-sex hormones may and often does result in significant mood and even physiological changes not encountered prior. But this shouldn't be conflated either with a menstrual cycle or with the effects of hormone replacement therapy (HRT) - that is, replacing hormones that would have naturally occurred but are depleted due to menopause, age, or various health conditions.
We've only very recently started to see wide public acknowledgement and analysis of how so many aspects of life (healthcare, urban and rural planning, product design, public policy, etc.) have been biased and women's needs overlooked for centuries because the focus has been on the male, almost exclusively, as the default human being. (See, e.g., Caroline Criado Perez's Invisible Women, Elinor Cleghorn's Unwell Women, or Misty Pratt's All In Her Head, just for a start!) Whether it's an unfortunate coincidence or an intentional disinformation campaign (or a little of both), statements like "Yes, anyone can get their period!", coming now, are a regressive step backward rather than a progressive step forward.
Modibodi didn't start this trend, but whether they are genuine "useful idiots" or are still blinded by a male-centered worldview and the data bias it engenders or are knowingly trying to capitalise on a (manufactured?) cultural "moment" for profit, they are doing actual harm (1) to women, who have the right to and need for a clear medical focus specific to our bodies and health without being buried again by the archaic "everybody = men" delusions of the past and (2) to trans people, who also have the right and need to discuss, understand, and communicate medical (physical, mental, and emotional) issues related to transition and to access help as required, without their experiences being conflated with other situations or obscured by opportunism, politics, or mythology.
Let's hope Modibodi reconsider their position and start behaving as responsible corporate citizens.