I wouldn’t call R’ S. Rephael Hirsch just “anyone”
IM(H)O, the main difference which causes the biggest stink is that in the 19th century people started labeling it. Before then, almost everyone except a few yechidim worked to support their families, and knowing science and history was considered the same as Torah, because it’s maaseh Hashem. To be able to give psak on complicated shailas, one must know anatomy and science etc. To give an educated decision, guidance and hadracha, one must know the history involved and be able to learn from similar situations in the past. (Everyone knows the story about the Netziv, where his parents were going to take him out of cheder and have him apprentice b/c apparently he wasn’t proving to be one of those yechidim – otherwise people were in cheder until about 10 years old- [this is where history becomes important])
People who are real MO (ie. actually orthodox and shomrei halacha to the fullest extent they know how/ are capable of) recognize this. Also as someone mentioned above it’s all about the emphasis. “Yeshivish” emphasize one’s personal relationship with Hashem, ie through maximizing Torah study, while MO may exert their efforts in other areas of avodas Hashem (although grounded in a solid foundation of past and continuing talmud Torah) such as chessed, making a kiddush Hashem, tikkun olam, and being able to support Torah institutions and other Jewish initiatives around the world.