I do agree there is no need to panic or to begin the process of leaving Thailand because of tax, but there is no way that you or even "experts" know how this is going to shake out yet. We'll need to wait.
As far as how Thailand Revenue is going to deal with US or UK taxation specifics, keep in mind if they start going after expat foreign sourced "income" they'll need to be dealing with taxation peculiarities of every nation in the world that has tax resident expats here. How will they cope? My guess is that they won't even try to have the bandwidth for that. Which might mean they'll leave us alone OR it might mean they'll interpret income without any regard to home country details and force us to try to prove differently. Or something in between. I definitely wouldn't go for a Thai tax ID number yet unless or until they demand that we do.