Gosh, that's a hard one. I actually got behind in my dental visits and my dentist needed to take care of a filling before they would start cleaning my teeth again.
They want to extract ALL of your teeth or one or a few? You don't have the money to do it? I am sure removing all of your teeth would be traumatic if that is the suggestion but what state are your gums and teeth in? Perhaps a cleaning isn't a good idea because of the fragility of your teeth? Could the pressure of cleaning be too much for them? Is that why they insist on extraction now? Or is your health in jeopardy because of possible future infections? More information would be helpful. If you are going to extract them, is cleaning even worth it?
Yes, any doctor can refuse to treat any patient for any reason.
It may be that the one you saw felt that leaving the other teeth would not address the problems.
A second opinion with another periodontist would be in order.
Hello~Doctors can refuse if they truly feel they would be doing the patient harm. However, I would certainly get a second opinion.