Q. To create a fictional series or movie loosely based on events surrounding real people and sports teams eg, if the lead characters are fictional characters who work as groundskeepers at Fenway in the 80's, would I need to get permission of MLB to use the logo or interact with actual people that are still alive? I understand most sports teams won't permit use of their logos that might portray them negatively, so in cases like the Ted Lindsay movie about the creation of the NHLPA, or baseball movies like Babe Ruth, how are these made?
As we used to say in computer science, this problem is non-trivial. Copyright is fairly straightforward (though "fair use" is not entirely well defined). But here you're looking at trademark right and privacy rights.
You can't use the MLB logo in a movie, whether positively or negatively, without permission. Nor can you use the Red Sox uniforms. They're trademarked. Your producer is going to have to get permission from MLB and the Sox to use those trademarked logos and clothes and such. Fenway may or may not be trademarked; sometimes stadiums and other icons are trademarked.
You can fake it to some extend. On BON COP BAD COP, we had a team that wears blue and white uniforms, and a team that wears red and white uniforms, and you were free to assume they had something to do with the Toronto Maple Leafs and the Montreal Canadiens, but we never actually used Leafs or Habs uniforms. The team name "Yankees" may be trademarked, but (I believe) you could call them "the Pinstripes" or the "Bronx Bombers" or "the Bronx Zoo" or "the Evil Empire" -- nicknames are generally not trademarked. (I can't think offhand of any Bosox nicknames that wouldn't infringe on the Red Sox trademark.)
You definitely can't portray living people negatively without inviting a lawsuit. That's why the two main characters in BACKBEAT are John Lennon and Stu Sutcliffe. At the time, Paul, George and Ringo were all still alive. Dead people have neither privacy rights nor can you libel them.
I believe you can portray living people positively, in an incidental way, without getting their life rights. (But I am not a lawyer, and nothing on this blog should be considered legal advice.)
Note that you can still write, and circulate, a script about the Sox. Circulating a script is generally not felt to be "publishing," and you're free to do lots of things in a script that you would not be free to do in a movie or a published book. You may be leaving a producer a bit of a headache, but in general I would recommend letting producers decide whether a given headache is too big for them, rather than shying away from a subject you love.