Claiming refugee protection in Canada as a US citizen on account of being trans is an uphill battle.
This is a judicial review that was granted on the request of the Minster of Immigration overturning an IRB judgment granting a trans woman refugee protection, and her claim was based on a risk she faced from her ex-roommate that was specific to her. Without that, and just on risks general to trans people, it'd be even more difficult to get refugee protection.
You'd be much better off as an economic migrant.
- If you work a skilled job, look into CUSMA work permits.
- If you have a degree, you might be able to get permanent residence status straight if you learn French.
- Even if you don't get PR, learning French can get you a work permit without an LMIA.
- If your education or work experience isn't enough to get you into Canada yet, look into study permits.
If you apply for refugee protection, you'd effectively be barred from any form of economic migration pathway that involves an intermediate temporary residence step since one of the requirements for being granted temporary residence status is that you'll leave Canada at the end of your authorized period of stay.
It's unlikely you'll be able to bring the rest of your family with you. Once you're a permanent resident, you might try to sponsor them, but that takes ages and you probably shouldn't count on it. Especially your brothers since there's no pathway to sponsor siblings unless you don't have anyone else you can sponsor or who otherwise lives in Canada.
The situation might change with the implementation of Project 2025, but as it stands, it's unlikely that you'll get granted protection as a trans person. The biggest hurdle would be the availability of an internal flight alternative where you'd be able to move to a blue state which generally have strong protections for trans people.
