I believe that if they used their political/social power to commit the crime, then no

If they use their privilege and influence to take advantage of people, they shouldn't be in government. But, if the crime was committed before running, then it is important to think critically about it. If we completely disallow it, then it would lessen the chance that an at-risk youth has of seeing themself represented in government. People of color are often convicted of crimes, and get longer sentences than white people.