Extracurriculer activities are meant to relieve stress from things in school. They are not mandatory, and if someone needs to focus on grades, it should be up to the parents to make that deccision. Not all extracurriculer activities are in school and while maybe in school after school activities could have a c above average, out of school activities should not
Extracurricular activity participation is not a right. It is a privilege that must be earned by proving that you can maintain your education while still improving yourself in your activity of choice. Yes, there are great benefits to participating in sports and other activities (like debate, chess, etc), but those benefits disappear when basic education suffers. This in no way means that I am in favor of the Government Schools that we have here in America. I am much more in favor of school choice through vouchers (But that is another topic entirely).
No, the C-average rule for eligibility in extracurricular activities should not be abolished, because students need to learn that participating in extra things is a privilege that they can earn by doing well in school. Besides, an A student should have preference to be on a sports team, over a C student, because the A student has been working harder in the classroom.
While I fully believe that extracurricular activities are a part of a person's education, I feel that if someone is not getting a "C" or average grade, that person should not be eligible to participate in extracurricular activities until their grade is at a "C" level or above. Young people need to understand that education is important and that there are consequences for not doing well. If a student is trying really hard, getting tutoring or extra help from the teacher, and doing everything a person can do, then maybe an exception could be made.