IITFT
do you really believe a shift from life revolving around beis hamikdash and karbanos to today is merely “minor sociological details” ?
Of the shisha sidrei mishna 3 of them are barely relevant* in our day to day lives namely Zeraim (aside from berachos), Kodshim and Taharos (for the most part). Half of what was practical in their day to day lives is no longer relevent day-to-day. Do you really view that focus on tuma/tahara was just a “minor sociological detail”
If your only criteria is “Do haredim today have the Same Goals, Destiny,and Purpose, as the past or Not?” Depending on how you phrase those goals, destiny and purpose I think all orthodox JEws and (probablly even many non-orthdox) will say they have similar goals: Get close to Hashem, fulfill Ratzon Hashem, make the world better place. IT is primarily the MEANS (what you call “minor sociological details”) of achieving those goals that separates various streams of Judaism
(*please dont misconstrue this as belittling the mishnayos r”l, I mean purely regarding practical day to day living)