For ID cards specifically most of the hostility was towards Blair's specific implementation which had a wide-ranging database that pretty much everyone and their dog in the public sector and beyond would have access to. While the arguments are perhaps a bit weaker in the modern day where the government taps the internet backbones and surveillance is a major category of business model, there were definitely good arguments against Blair's proposals that weren't necessarily applicable to ID cards in general.

I don't think it's necessarily Thatcherism that made people like this, just a slow erosion of trust that the government has the competency to carry out the tasks of a modern country that's accelerated as time's gone on. Anecdotally Liz Truss's episode as Prime Minister seemed to be the final straw for a lot of people's goodwill towards the government.