I think that as with everything else it will depend on whether the media take it up.
So far all the right(?) wing papers have printed articles about the survey, ie Telegraph, Mail etc..
The results will only get traction if a radio or tv interviewer uses it as a basis for a question.
And I am afraid to say the media interviewers are usually so dumb or think we are so dumb that they couldn't manage a slightly more sophisticated question than the nice simple one of can women have a penis.
To try and frame a quesiton that says Labour supporters actually want the Tory policy of single sex spaces and the GRA, what is your comment is unlikely to be asked.
Dont forget, over and above how inadequate many of our politicians are, the biggest failure in this country is the abysmal standard of reporting. Everything is dumbed down to personalities etc..
However, for the future, we are going to need this information once Labour and their ex Stonewall politcy director starts to make getting a GRC easier.
I included the relevant link to the Sex Matters web page for anyone who wants to download or copy.
Even just the charts.