I has a similar issue, when I was getting invited to join Apple Developer Program. I tried joining through the invitation link and I would always get the "We can't process your request" message.
The solution was to:
Log in to an iPhone/iPad with that particular Apple id.
Try to install an app.
You will get a terms and condition pop up that you should accept.
Install the app
Wait for a while until Apple fast servers update your status (around 1 hour for me)
Now you should be able to proceed without the weird message.
Topic:
App Store Distribution & Marketing
SubTopic:
App Store Connect
Tags: