“Should men be allowed to participate in sports events for women and girls?”
Really the most appropriate response to this framing is that men aren’t participating in women’s sports.
We all have both sets of the genes that control whether our bodies express male or female secondary sex characteristics. We’re born with both male and female genetic code and it never goes away, it’s simply a matter of which are being expressed and which are not.
The reason HRT works is because tipping the hormone balance from majority male to majority female or vice versa is telling the trans persons body “express female/male genes now” which results in real biological change, the same changes that cis people experience, the same genes that would be active were the person born as their target sex. After transition, trans people are biologically closer to their target sex than their birth sex, the literal tissue of their body has changed.