Poor FPS in game while streaming
Solution 1:
I'm going to make this an answer so I can give a more complete and better formatted reply.
First off, keep in mind that most popular streamers usually have a separate computer dedicated toward streaming. This requires a significant investment!
In order to immediately improve your performance you should put minecraft at the lowest possible settings as well as look to reduce the compression ratio of OBS. Higher ratio = more work for your CPU = FPS lag/drops. I'm at work at the moment, but when I get home I could look into it further. Don't worry about burning out your CPU either. The only way that would happen is if youre trying to overclock it or if its just faulty. Feel free to adjust the priority, just understand that it can negatively impact the performance of other programs including OBS. If you prioritize Minecraft you run the risk of taking processing power from OBS which will cause your stream to lag.
Having a good rig doesn't always guarantee the ability to stream either. I can hit about 200 fps in league on my computer, but if I try streaming I get a considerable performance drop along with a nearly imperceptible delay.
I'll add onto this if anything else comes to mind as my caffeine kicks in.