Well I tried copying everything on my SD card to my computer and Formatting my SD card through the phone, and then replacing all the backup files onto the SD card. This didn't solve anything. I tried uninstalling RingsExtended, Ringdroid, and Ringlert. This didn't solve anything either.
So I decided to just start fresh and delete all of the custom tones I was using and either redownload them through Ringlert or make them again/make new ones with Ringdroid. After making new ones using Ringdroid it will allow them to work just fine.
Ok I can't stop fiddling, but in this case it was a good thing. I have one clip that I'm using as my phone ringtone that I got through Ringlert (The Invader Zim Doom Song). But if I set this as my General Notification tone by using RingsExtended or through Ringlert itself, this ringtone will override the settings for Gmail and SMSPopup. I tested this with a few other things from Ringlert and it they all do the same thing. So that must have something to do with where they are stored, although it's a toplevel folder on the SD card.
But thankfully if I use Ringdroid to modify any of these audio files into a Ringtone/Notification they will then show up under the Default Android Ringtone/Notification picker, and if I set any of these newly edited tones for my General Notifcation tone then the others (Gmail and SMSpopup) will work correctly no matter if they are directly from Ringlert or edited through Ringdriod.
So if you are having any issues like this, try this and if this doesn't help then I'm at a loss. Try downloading Ringdroid and using that to make these sounds files into Ringtone/Notification tones. Once they have been edited they should show up when you use the default Android tone picker. And if it works for you the same way it did for me. This should solve your problem. Although if using the sound files you already have doesn't work. Try finding new ones and using Ringdroid on the new sound files and see if that makes a difference.
Best of luck!