Whenever I open an RStudio Project (e.g. by double-clicking) it not only starts RStudio (or switches to the project when opening a project from inside RStudio) but also starts Microsoft Publisher, which then of course fails because Publisher cannot open the file.
I'm not sure why this happens and how to resolve this so that Publisher does not start anymore. Any help appreciated!
A bit of extra information would be helpful in diagnosing this issue.
It was originally posted in rstudio-cloud, but I think that was a mistake. Your text suggests that you're asking about the RStudio desktop. (RStudio desktop is the RStudio IDE on your local machine. RStudio.Cloud is the RStudio IDE via the web, at https://rstudio.cloud and soon to be at https://posit.cloud.)
Based on what you've said, it sounds like an issue with your local machine thinking .Rproj files should be opened with MS Publisher. If that guess it true, you want your .Rproj files to only be opened by RStudio Desktop.
Here's a guide on how to check and change your file extension default program settings in Windows,