When referring to a sports league like the NFL or NASCAR, would you use "it" or "they"?

This is a great question! The short and simple answer is
that using either it or they
to refer to a corporation is correct. However, meaning is encoded in
language, and so using one term instead of the other implies very different meanings.
Let's start by looking at the definitions for both of these
words:

It is a
pronoun used to describe inanimate—or
nonliving—objects.

Ex: The NFL says
it will donate over $1 million dollars to the American
Cancer Society.

They is a
plural pronoun and is used to describe
people.

Ex: The NFL says
they will donate over $1 million dollars to the American
Cancer Society.

Both of these sentences are
grammatically correct. The difference lies in the implied meaning—using
they to refer to corporations adds a human quality. Do you
feel that these corporations are human?  If not, then use
it, which implies that entities such as the NFL, NASCAR,
Coca-Cola, or Proctor & Gamble are merely objects, and should not be
personified. Remember that both terms are correct, and this is more of a matter of
voice—how do you want your audience to perceive these entities, as faceless firms or
caring corporations?

*A special note: Academically,
scholars agree that they should only be used in the plural
sense; however, they is used in informal English singularly
as well.