They try not to be elitist in their selection process, but… 

“We aim to reflect the breadth of filmed expression. We try not to be restrictive or snobby about what kinds of films are appropriate. An auteur classic, a Hollywood blockbuster, and an independent B horror film all have to be taken on their own terms. All we ask is that each film in the collection be an exemplary film of its kind. Of course, we can’t just pick movies and put them out. The process of getting the rights to release a film can take years. Even if we want a film, we can’t work on it unless the film’s owners grant us the rights to do so.” - Criterion’s FAQ page

But film scholars, journalists, and regular movie-lovers have pointed out that the collection is heavily skewed towards North American and European movies directed by white men.Last year, The New York Times found that of 1,034 feature-length films released by Criterion through June 30, 2020, ~11% of directors were Asian, ~7% percent were women, 2% were Latino, and less than 1% were Black (exactly 4 films by African-American directors and 4 by Black directors from outside the US, including the only Black female director represented). I can’t find anything on Indigenous, trans, or gender non-conforming filmmakers. This infographic of the collection by country is a bit older (2014), but the trend is still true: