[CW: Discussions of Transphobia/Unsolicited Sexual Behavior]
A "leftist feminist" who disagreed with something I said accused me of having "male privilege" even though she knows I'm transfeminine. She said that "all male people have male privilege," with the term "male" there including transfeminine people. To do some harm reduction, she said "I didn't say anything about your gender, just your maleness."
What's really the kicker is that, even if you like to use this awful "sex and gender are different things" as a means of trying to have one foot on the transphobe side and another foot on the trans ally side, the idea of transfeminine people having male privilege from a systemic point of view is just deeply unserious.
I lost my family, got called queerphobic slurs by them in the process, dealt with extended periods of joblessness while also fearing the potentiality of being homeless with basically no support but Hexbear, and have gone through various other abuses because of my transfeminine identity, including uncomfortable sexual scenarios with men, and I have male privilege?
Well, let's not forget that she was also 
I think the sex v gender thing can be valuable as a little white lie to help people begin to understand without getting too complicated—kinda like how kids often don't learn about plasma when they're learning states of matter because it's kinda confusing at that stage, or how physics problems often assume an impossible frictionless environment to make learning other elements easier.
No, teaching people an incorrect model first necessitates re-educating them later or else they're going to cause issues. This isn't like Newtonian gravity and relativity - a brief explanation of the social construction of sex can be done in just a few sentences.
whether or not such an explanation can be done is immaterial - what matters is if people are actually going to buy into that explanation. "sex = bio vs. gender = social" is fairly graspable for people because it's offering a granularity that doesn't inherently contradict their previous understanding. the moment you bring out "social constructs" you're going to lose people, especially when it's blowing up a hegemonic notion they thought they've had covered since like age 7
We're not losing anyone. The "allies" unwilling to engage in analyzing sex are going to be calling me biologically male and telling me I can't play sports anyway while they politely she/her me.
I'm more talking about the people who have no idea what a transgender is. You're right in that if someone purports to be an "ally" they've signed up for learning things the more complex way
states of matter is a great analogy because there are way more than four of them too