I suspect one of the reasons the consultation is being run the way it is (under the radar) is because of the success the TRA lobby has had in positioning self ID as "just like gay marriage, it only affects people who are trans". Thus they have created, up front, an environment in Whitehall which dismisses dissenting voices towards self ID as being just like extremely socially conservative/extreme religious objections to gay marriage. Because of course in the case of gay marriage the come back of "well, it doesn't actually affect you - don't like gay marriage, don't have one" is actually an unanswerable comeback.
However self ID is not like this. It does affect other people. Suppose my firm had a Pip Bunce working for us. On Pip's "Pippa" days, Pippa could come to the workplace gym, saunter into the women's open-plan changing room (where there will be women naked) and get Pippa's penis and balls out. Women who didn't like this - whether because of past sexual abuse, religion, or like me, because they simply didn't want to be naked in front of a man who wasn't their sexual partner - would have two choices: grit our teeth and shut up; or stop using the facility. (Because conveniently Pips apparently has weeks where he feels more manly and comes to work as a man on most days, and weeks where he feels more womanly and comes to work as a woman on most days - so you couldn't even try to work round his pattern, because he has none, everything is done according to his whim).
And that's only a trivial example - there are of course the much more serious examples of women's prisons, closed psychiatric wards, homeless shelters, DV shelters, rape crisis centres.
Self ID is NOT like gay marriage: self ID genuinely affects other people, specificially women.