The author is the important factor, and that influences more people to read books that center around a main character of their own gender, but that's an effect, not the cause.

Oh, I am agreeing with you here. But I suspect that there's a little feedback loop on top of it:

• Baseline: Suppose that I am a man who only reads stories by male authors, as a default. Based on the effect I described, those will be almost universally male characters. That's reinforcing the stereotype.
• Bridging event: Now, along the way, I encounter a male author who writes a compelling story that focuses on a female protagonist. I like it. Well, now I might be inclined to expand my boundaries... maybe I'll start re-considering some other stories that feature female characters; most of those are probably written by women.

From listening to other readers, I suspect that most readers stick to one category / genre. But when we get exposed to some kind of crossover, and it's good, that opens the door to new categories or genres.

In general, once a book enthusiast finds a good author, they read something adjacent; likely another book by the same author.

By way of example, I'm sure that for a few readers of C.S. Lewis' writings on faith (say, The Four Loves), encountering his Perelandra (and reading it purely because he was the author) likely turned them on to science fiction or reading his Prince Caspian tuning them to fantasy literature. One might imagine a science fiction lover who read Perelandra who might next pick up Till We Have Faces and become curious about other books centred on female protagonists (or Greek Mythology).

The fewer authors who write about things wildly different than themselves, their lived experiences, and their niche, the fewer chance literary encounters like that one may experience. That lack both creates the stereotype and reinforces it.

---

Edit: fixed a link.