Build 36.0.3 Just arrived on my device and seems to have corrected the problem.

UPDATE: This only lasted for the rest of the night. By the next day, the issue had returned.

Warewolf said

Starting on March 20th, both my Nexus 4 and my Nvidia Shield tablet will not load past around 15% for any website unless I select Request Desktop Site. This only seems to be a problem when the devices are connected through wireless data. Wi-Fi is unaffected by this issue. I've force stopped Firefox, I've cleared data and cache, and I've removed / re-installed Firefox. i've also rebooted the devices a few times. Google Chrome is also working fine.

This is once again happening on my device. Pages load fine when I check the box for requesting desktop site, but do not load otherwise. Hangouts, and other online activity are working fine.

I continue to have no success using Firefox on my devices while using data. Oddly I have noticed I can use google, and I am now using this site while in Firefox on mobile, yet no search results will load, and none of my bookmark or directly entered URL work. It appears that even the beta version does not work. Chrome does work though, as do all other online connections. Desktop pages are no longer working either.

I activated a different carriers SIM card to work on addressing some coverage issues, and noticed that mobile data is working perfectly fine. Perhaps the other carrier was blocking my usage? I'm not sure I could believe that they somehow only blocked firefox, but thats my story and I'm sticking to it.

I've just been given more motivation to change carriers, and will consider this closed.