Read the text and judge for yourself how the diacritical marks affect readability.
Rather, the removal of them affects readability in a similar way to removing accents, punctuation or writing in all lowercase.
Now, I should add that for an article that is specifically about language, and even has some illustrations of the meaning of these diacritics, this is almost certainly a bad choice on the NYT's part. But as a general rule, I think it is defensible.