Meghan, my response to that is... Show me the crossdressers who are trying to educate the public on that difference, rather than insisting that they should have the same types of access and legal recognitions (as women) that trans women need. I'm choosing my words carefully for forum rules reasons.
To put it incredibly mildly, I haven't seen them. I've seen the public narrative from the trans community continuing to focus on the transexual narrative for sales purposes, while also insisting on incredibly broad legal definitions that serve only to include crossdressers in ways that directly contradict the fact that (by any definition) they are men. I literally cannot tell my cis friends that the trans community is not lobbying for men in dresses having certain kinds of access. I would think that if CDs were sharing the burden of education and exhibiting some empathy for and understanding of women's concerns, they'd be jumping into those discussions and saying "Actually, no thanks. We're the men in dresses, they're women. This is about them."