I don’t know the full context, but I think I understand your feelings. Based on your descriptions, your parents sound very similar to mine. I live in a very competitive area where kids intern during the summer/school year, go on medical trips abroad, compete in science fair projects/FBLA/DECA…etc. However, my parents did not allow me to participate in any activities that required money and limited my volunteering times (Even though I was volunteering with only one organization). I couldn’t intern because my parents wanted me to focus on my academics even though I already had solid grades and test scores. They thought if I scored a 35 or 36 on ACT, then I would go to great colleges. In other words, my parents didn’t care about ECs-all they cared about were academics. How I approached this situation was by reducing my extracurriculars but focusing heavily on a couple. I also managed to get an internship by promising my parents that I would go to the library every day during the summer and stay until 7 PM. I still felt very uneasy about my lack of extracurriculars because other classmates were winning national awards…etc. So I also looked up for remote volunteering experiences like becoming a social media manager for non-profits (and did this secretly!). I also wrote about my circumstance in the additional comments section for Common App.
This is just how I overcame my situation.