New to WordPress: What causes conflict between wordpress theme & active plugins?

I am a new wordpress user and i have already run into a few hiccups.
I am curious what are some general causes of conflict between a wordpress theme and a plugin.
As an example, when I was playing around with the customization of a wordpress theme, it caused the maintenance mode plugin to lose the background image and font styles when I accessed the website from another browser.
I know it is something to do with the wordpress theme because when I went back to the default customization, the maintenance mode page worked fine again.
I guess my question boils down to what general tips you may have when it comes to customizing a theme without impacting plugins.
Thanks