I finally discovered why I can't copy and paste in RStudio: there's an interaction with Alfred's clipboard manager. I was noticing that every time I copy something from RStudio, it gets appended to the last thing I copied. Alfred has a feature where double-tapping C when you copy using Cmd-C appends the next selection to the most recent item in the clipboard. Disabling this feature resolves the problem. I guess RStudio must be sending a double-tapped C when copying.
I had eventually found the solution to my problem in an old post from 2014: https://support.rstudio.com/hc/en-us/community/posts/200679798--Mac-OS-Mavericks-Copy-and-Paste-Text-is-Appended-to-Clipboard
I just wanted others to find this solution more easily, and to make people aware that this is still a problem.