I think it pays to go back and understand the term modern orthodox, and there was another thread discussing this recently, I think.
In the early 1900’s Modern Orthodox and Young Israel and Zeiri Agudas Yisroel were all movements to help keep people frum. To fight against the especially strong tide of chilul Shabbos.
In the book about Irving Bunim you see a photo of his wife with her hair uncovered. Yet he worked with R Aharon Kotler and both he and his wife were very active in promoting Yiddishkeit. Just the times and a lack of knowlege meant the standards were much lower. Covering hair was a neglected mitzvah as was shatnez.
There are those today who call themselves modern orthodox, but are very makpid on halacha. There are also those who violate halacha in many ways, mostly from a lack of knowlege of the importance of various halachos. They continue keeping what their parents kept, but not more, not really having a strong connection to Yiddishkeit and mitzvos.
I think any serious Jew would agree their Yiddishkeit is lacking, but would look at them in a sense as a tinok she’nishba.
That is the modern orthodoxy that many Gedolim criticized – one of compromise or neglect of basic halacha.