I have both BOTI settings enabled and I have fast rendering in Optifine turned off but whenever I open the TARDIS, I just see a blank blue screen until I shut the TARDIS' door. I thought removing Optifine would fix the problem, but it still persists. Can someone help?

Other mods can also conflict with this. Most notably Shaders, but maybe BetterFPS as well. Which mods do you use alongside?

I have BetterFPS installed, but I didn't think it would cause problems. I don't think I want to remove it just yet. Also, I have a lot of other mods installed, I'm not sure if I want to list them all. So other than BetterFPS, I would like to know whatever kinds of mods would cause this problem. If there's nothing else that could cause this, then I'll remove BetterFPS.

It mostly conflicts with mods that alter the games rendering. BetterFPS probabydoes something along these lines to achieve a higher FPS, they probably do something similar to Optifines Fast Render option.

I'd suggest removing it and testing it out to see if it works. If not then try removing any other mods you have which you think might alter rendering

 After doing some testing, it looks like BetterFPS really was the culprit here. I removed it and now the TARDIS works properly, thanks.