English has a lot of phrases like that, where there are different words used to have the same meaning. The two phrases basically mean the same. If you want a difference then you could say "Let it be" means to leave a situation how it is. "Let it go" could mean to stop thinking about something that might be bothering you.
You could use either interchangeably and it's perfectly acceptable.
You can also say "Let him be" about a person, meaning leave him alone or don't bother him. For example, if someone is really upset, and I try to encourage him, but it doesn't work, another friend might tell me, "Just let him be. He'll calm down in a little while."
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