The law doesn't give you a pass because you are running a "mugshot website". If you are a private company calling people who have their arrest info posted on your site and you are charging them to take their info down from your site for a fee, then you are held to the Do Not Call requirement as is everyone else. Careful or you could end up on someone's site yourself.
18 USC 1030 - Fraud and related activity in connection with computers
18 USC § 641 - Public money, property or records
1. Whoever steals or purloins public records.
2. Whoever knowingly converts public records to their use.
3. Without authority sells public records.
3. Without authority conveys public records.
Keep pushing the envelope and you WILL get burned! This is probably a good time to get out of the mugshot business. You have made a profit, now your methods are about to be investigated and regulated. Along the way, someone will be made an example of.
Smart hustlers will move on to the next big thing, selling their businesses to investors who will get hit with all of the fallout.