Hi Evan,
I just checked the Menu styling options of the Responsive menu plugin on my staging. I was able to center the text and change the font weight etc. But I was not able to change the background colors.
At first kindly check for plugin or theme conflict on your website. The fastest way to rule out a conflict is to deactivate all plugins and switch to a standard theme like?Twenty Twenty. If this resolves the issue, you have a conflict and should activate one plugin at a time until you locate the conflict. Finally, after all plugins are active, switch to your theme. This will narrow down the conflict to a specific plugin or a theme conflict.
Kindly let me know so that I can forward the issue to our development team.
Regards,
Kriti