The fact we can't even agree that sex and gender are two different things is the final proof to me that the Right is arguing in bad faith. It's such a simple concept to grasp.
One podcaster was suggesting we use male/female/intersex to refer to biological sex, and man/woman/etc. to refer to gender identity. Such an obvious and non-controversial idea, yet it'll never fly with the transphobes.
I remember back when people wanted to use 'Civil unions' as the term for gay marriage, and have marriage be reserved for religious unions. Then they realized that they had to ammend 10,000 laws that specifically mentioned marriage. Apparently it was easier to change the definition of marriage then to alter that many laws.