From what I have seen, to my surprise, the NYT's opinion section does encompass diverse viewpoints and reports in general are neutral in tone!
Any criticism I have seen of NYT are either nitpicking (example: headline being too moderate) or taking an incident that is outlier and generalising it (example: Editor of opinion section didn't read a controversial opinion piece by a politician before publishing and resigned over the backlash. Instead of viewing it as an one-off incident, it was criticized as NYT not tolerant of diverse opinions).
NYT is not perfect (who else is?) but it is still one of the best organization with highest standards of journalism I have seen.