MAMP and Valet can conflict if they're running at the same time. I believe this is due to them both trying to write domains to host files simultaneously. I've written some basic instructions here on how to deal with this. Basically, you need to make sure they're not running at the same time.
They can still exist happily side-by-side though. I found it easier to leave Valet’s config alone and instead make sure MAMP is not bullish.
Bear in mind Valet silently starts up automatically every time you log into macOS. So you want to make sure MAMP does not also automatically start its servers when macOS starts. To do this:
In MAMP go to “Preferences > Server.”
Make sure you untick “Start Apache and MySQL on system startup.”
This should also stop MAMP firing up when your system starts.
If You Want to Use MAMP
You need to make sure Valet is not running.
Open the Terminal application in macOS.
Type “valet stop” (without the quotation marks). You should be prompted for your system password. Enter it, and Terminal should inform you that Valet has stopped.
Once Valet has stopped, you should now be safe to click the “Start Servers” button in MAMP.
If You Want to Use Valet / Statamic
You need to make sure MAMP is not running.
Open MAMP and click the “Stop Servers” button in the top right. This button should not be green.
Once MAMP’s servers have stopped, you should now be safe to start Valet.
If you had previously stopped Valet, open the Terminal application in macOS. Type “valet start” (without the quotation marks). You may be prompted for your system password. Enter it, and Terminal should inform you that Valet has started.