Law schools may not "care" about ECs as a major tipping factor in the law school admissions process, but it has been my experience over many years (including my time in law school) that the vast majority of law students who have been successful in law school and who are most desired by law firms when it comes time to make hiring decisions do, in fact, have "ECs".
These ECs may take the form of past work experience, leading initiatives to get rules changed or created, community involvement in one form or another, clubs/organizations (often in leadership positions), playing on sports teams (school or recreationally), running marathons (or shorter distances)/doing triathlons, caring for ill family members with real responsibility for their needs, participating in election campaigns, etc. Military service is also highly prized. The list goes on and on. Any involvement in that shows dedication, hard work, an ability to see things through tough times and an ability to reach goals is highly prized. It doesn't have to go so far as to have won a Pulitzer Prize or the Medal of Honor for employers to take notice.
My response to students that I counsel when asked to help them "find" ECs is that they should participate in ECs that are meaningful to them and in which they will have the opportunity to develop their leadership, planning and teamwork skills. Law schools may not give you a lot of credit for participating in ECs, but they do generally notice when you have not participated at all. Employers will value the skills you have demonstrated through your ECs, particularly if you have not taken time off between undergrad and law school to work.