Exactly - the left is fighting for the rights of oppressed groups, one of which is trans people. So being in favour of trans rights would therefore make you left wing.
That's rather begging the question, isn't it? How exactly are trans people oppressed, and what rights are you in favour of?
You could argue that billionaires are oppressed by having to pay tax, and arms manufacturers are oppressed by export controls, so fighting for less tax for billionaires or fewer export controls for arms manufacturers would make you left wing.
As trans people's claim of oppression seems to basically be "other people know what sex they are, and sometimes act accordingly", it would seem to fall into that same category of grievances.
Responding to someone's grievance or demand for special treatment is not inherently left wing. It depends what the demand is.