I like thinking too hard about this topic and something I never hear people mention is dehumanization.
In America, rats were used to portray "undesirable" groups of people in propaganda. Their presence was depicted as a plague, and they were the pest spreading it across the country. Rats are also positioned around undesirables in art, such as the homeless and witches.
Now consider the rhetoric around transgender men transitioning: trans men are victims of the trans plague, confused tomboys infected by the woke mind virus. But infected people are only pitied from TV screens, not up close and personal. "Transgenderism" spreads with minimal exposure. An example of this is if you've ever gone to school with a single trans friend and was then told by your parents they made you transgender.
Second all of that with the fact that transgender people are also more likely than their cis counterparts to experience homelessness. And the cherry on top... lgbtq relations, "cross dressing", and gender nonconforming behavior was affiliated with witchcraft in many countries... And it kind of makes sense why some trans men affiliate themselves with rats.