On the topic of Modern Orthodoxy, here is an excerpt from an English letter of the Lubavitcher Rebbe from Adar 5738 to a woman who was becoming frum.
(Disclaimer: Obviously, the exact definition of Modern Orthodoxy is blurry, so I doubt that everything written here applies to every person who calls themself MO)
“P.S. Your using the term “modern orthodoxy” prompts me to make the following observation.
Although this term is frequently used, if you reflect on it you will realize the inner contradiction in terms. For, orthodoxy refers to a full commitment to a life regulated by the Torah, Toras Emes, and its Mitsvoth, by which Jews live, whereas “modern” implies a compromise and adjustment supposedly in keeping with “modern” ideas. But where truth is concerned, there can be no compromise or accommodation, for even 99% of truth is not the whole truth, and therefore not truth at all.
Needless to say, 99% is better than 98%, but one must not delude oneself in believing that it is the whole truth. Indeed, the Rambam rules that if a Jew accepts the whole Torah except one letter, he is deemed as if he denied the whole Torah. And one of the explanations of it is that truth and compromise are contradictory.
The above does not mean that unless a Jew observes all the 613 Mitzvoth, he is not an observant Jew. Indeed, the Torah declares, “A Jew, though he has sinned, remains a Jew.” It states further that no sinner is rejected, and eventually everyone who had strayed will return to the fold. What is emphasized above is that any thought that the Torah is in any way “outdated” and needs to be “modernized” that is heresy and a denial of the Divine origin and eternal nature of the Torah and Mitzvoth. There is surely no need to elaborate to you further on the above.”