The short answer is: you can't. I emailed MAMP's support directly about this question and was told very bluntly "you can't and we aren't adding an option to stop it." What I did was install the "Tab Auto Close" browser extension and added a regex rule as follows: "https://www.dropbox.com(.)*127.0.0.1". This auto closes it for me, but you may have to adjust the regex expression depending on the URL it opens for you.

Really scummy practice from MAMP if you ask me.