I think some Tory MPs are very focused on Brexit and don't know much about self-ID so far. And it is being sold as a small admin thing that only affects a few people who let's face it, are unlikely to be core Tory voters. So a lot of MPs think that it is safe to ignore.
That's why the other MPs and lobbyists are pushing so vigorously to get self-ID passed. Precisely because the other MPs are distracted and have their eye off the ball at the moment.
They know that as soon as MPs can look at the issue properly, like a lot of ordinary people are now beginning to do, then the whole thing falls like a house of cards.
By this time next year there will be plenty more tales of male sex offenders identifying as transgender. And trying to get self-ID in under the radar will get more and more difficult with every week that passes.
Rushing it through by telling lies and silencing debate is their only hope.