RetroPlug loads just fine here in both OpenMPT 1.30 and 1.32. Can you figure out which is the first OpenMPT version it doesn't work in for you?

Sounds like it could be potentially related to 0001912 where another user had issues with a specific plugin GUI, but it's working just fine on my machine as well. Maybe something with graphics drivers?

I have tried versions inbetween and also the latest version I have been using so far (1.32.03.00) - redownloading the portable zip.
It turns out that the versions that you extract from the zip work fine, but the version you install through the setup program freeze.
Checking the "About OpenMPT" there is no difference between them.
So it does load fine, but for some reason, only if you got the portable zip version.

So the difference is probably that the installer version is installed to C:\Program Files, while the portable versions you put in a different place. They would probably also stop working if you moved them to C:\Program Files. Can you try that? Vice-versa, copying the installed binaries to some other location would probably also change the behaviour.

This smells more and more like some component other than OpenMPT and RetroPlug is involved here - as mentioned before, maybe graphics drivers, or maybe anti-virus. I don't have the issue both with a portable and installed version on two different systems.

I extracted them all in the same location, that is C:\Program Files\OpenMPT\OLD_VER giving each version its own subfolder with the OLD_VER folder.
I did disable my antivirus to test and it does not seem to be the cause. I am also uncertain whether it would be the graphics driver, considering, that it only does not work for the installed version.

The binaries between portable and installed versions are 100% identical. Just the packaging is different. Graphics drivers sometimes do special treatment of programs if they have a specific name or location, that's why I think it could be related.

I see there haven't been any updates to RetroPlug in a while, so I guess it's unlikely that the author can help out. I will see if I can compile my own RetroPlug build and send that to you, because that would allow us to create a memory dump and see where exactly the plugin is hanging.

Okay, this was all but trivial but I managed to compile RetroPlug: https://sagagames.de/stuff/RetroPlug_vst2_x64.7z

I have debug symbols for this version, so I will be able to inspect a memory dump from OpenMPT to see where it's hanging.
Please use this version of the plugin to reproduce the problem, and when OpenMPT hangs, open Task Manager, right-click the OpenMPT and choose "Create memory dump file". This will tell you the location where the dump was saved to. I'll need this file. Unfortunately it's way too big to attach it to the issue tracker here, so you'll have to find another place to upload it to. Note that it compresses quite well with either 7z or RAR, but the resulting file is still going to be huge.