According to this, the GitHub Problem Report does not look like you can remove the Projects tab in the same way as the pull requests tab. Github should set a parameter where you can remove this tab, since many repositories do not use this new Github feature. I will contact the GitHub contact page shortly to get this problem.
As of 10/28/2016
They said that this would be considered one of the main claims for Github developers, as stated in a statement:
Hello!
I have a question on how to remove the projects tab from your github repository. Is it possible? Can you guys realize this soon? I already asked a question here: How can I remove the projects tab , and there is also a github problem. If you can tell me more, that will be useful :-)
This is currently not possible. Thanks for the offer! I added it to our list for our team.
Thanks, GitHub Staff
Unfortunately, at the moment it is impossible to remove the project tab :(.
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