Meaning of “liberties taken with the word”

Lexico "take liberties"

1 Behave in an unduly familiar manner toward a person.
you've taken too many liberties with me

2 Treat something freely, without strict faithfulness to the facts or to an original.
The scriptwriter has taken few liberties with the original narrative

The word "liberty" means freedom. To take liberties with is to act too freely toward someone or something, The sense of
Not all researchers agree with the liberties taken with the word.
is
Some researchers think that the word has been used too freely, in a way not faithful to its original meaning.

Note that if you are dealing with an idiom, some dictionaries may have a definition for it in its simplest form. The definition above was found by looking at "onelook.com" for "take liberties".