It's grammatically correct. Whether it "makes sense" depends on the context.
It is related to romantic relationships.
Lover is telling her beloved " either stay with me or leave, but if you stay, don't pretend to stay with me.
By "either be", the writer( a friend) he means "either stay with me".
You have told that I meant stay, but I did not mean stay; I exactly meant exist.
And one more point, if they say it is wrong (and they have not), they are in fact saying that the Shakespeare's phrase: "to be or not to be." is wrong.
Incidentally, I do not have more time to argue with you about this subject.