Can I as a realtor in washington state sell a home where I am one of the two court appointed executors to the estate?

As long as you aren't charging above-market rates, and you get fair-market value for the property, you'll probably be okay. Keep in mind that probates make people crazy sometimes, and some people will fight over anything and everything. If you have concerns about the heirs/beneficiaries challenging you, you could ask them to sign a consent/waiver acknowledging the situation.

Since you are co-executor, you both should agree on who will list the property and the price. If you have non-intervention powers, you have power to sell and bargain on behalf of the estate. since there is a potential conflict with your serving as the realtor and getting a fee for your services, you should not only have agreement with the co-executor but also inform the heirs/beneficiaries of the estate and give them an opportunity to object. If they do object, you should go to court and get a confirming order of your ability to sell, lay out what you will charge and the listing price so the court can approve.

Ms. Singleton laid out the issues well. You should consult with a probate attorney.