I think a lot of remain Tories are lying about being remainers (including Cameron).
I'm afraid this is nothing more than
post hoc rationalisations of
feelings. Because you
feel that Remain is ("must be") the 'progressive' choice, and since you understand Tories as being
not progressive, therefore Tories can't be Remain. But the reason the conclusion is incorrect is that both the first and second premises are faulty.
You strongly believe Remain to be the Progressive choice, but you are not allowing all the evidence against Remain. You merely feel that it is the internationalist choice, therefore it cannot be anything but progressive. This despite knowing about Fortress Europe, about the neoliberal nature of the EU rules, about the treatment of Greece and the periphery (Portugal etc), and despite knowing that Remain was led by a Tory prime minister and chancellor. But this must be black and white, right? You have to choose Remain or Leave, and the decision has to be clear cut...doesn't it? One is the left choice and the other the rightwing choice. (Well, how about, no: it isn't that simple).
Still on premise one: you are not clearly defining "progressive". Remember, the Tories under Cameron passed the Same Sex Couples Act, and so on. Indeed, neoliberalism successfully co-opted many of the individualist concerns of identity politics. So "progressive" ideals can't be seen simply in left and right shorthand any more, as far as mainstream UK parties are concerned. They are no longer a reliable marker of leftness.
Which leads us to the problem with premise two: that the Tories aren't "progressive". Well, we already know that we haven't defined that well enough to exclude Tory policies. So it can't be used to rule out Toryness. And secondly, it misses what is the primary concern of the Tory party under Cameron and Osborne: the neoliberal project. Look at who else supported Remain - the CBI, the British Chambers of Commerce, the financial institutions, and so on. The neoliberal project, in other words.
Which means that your feeling that Tories couldn't have been Remain is based on a number of errors, failures to properly define terms, and a lack of structural analysis. But mainly it was just a
feeling that you couldn't possibly feel this strongly about something that Tories also cared about.
What you should be watching now, however, is the way that the neoliberal project copes with coming to an accommodation with Brexit. That's what is at the root of the Tories' turmoil at the moment.