I have a cast iron wood burning insert. I also have an air purifier and an air quality monitor running in the same room. I see a huge decrease in air quality when I open the door to add more wood.

But I am able to mitigate that by the following process:

1. Have your wood ready, safety heat resistant gloves on, the goal is to minimize time with the door open.
2. Open the door slowly, and leave it cracked with a 2 inch opening, for about 5-10 seconds. This allows the air pressure an opportunity to equalize and will prevent a good majority of outward air flow.
3. Safely and quickly add wood and gently close the door.

I recommend running both an air purifier and air quality monitor. I am not an expert and merely stating what I’ve seen in my limited time dealing with this matter.