What advice do you have regarding park touring during marathon weekend? Should certain parks be avoided on certain days/times?
As others have said, the pandemic makes this a very wild guess. My best recommendation would be to select the park(s) that are most important to you for post race medal photos/meals as your priority for the day and then roll with whatever comes crowd wise.
This is admittedly the wrong advice, but when I did Dopey in 2019 it was part of a family vacation. So it was races in the morning and parks at night. I didn't avoid any parks or any activities. I just treated it like a normal Disney trip.
Aside from the late nights, this is more or less how I've treated the parks when there for races. I do allow myself a whole lot more time sitting down or watching shows to rest my legs and try to avoid long standby lines. I usually head back to my resort for bed around 6:00 or 6:30 so I can be in bed by 8:30 or 9:00 for the race. It works for me.
The big thing to consider isn't really the specific parks and days but the energy you'll be expending compared to your race. If you are new to running and are worried about being able to stay ahead of the sweepers I would save my park days until after your race.
I will say that it really comes down to knowing yourself. I had run 5 different multi race challenge runDisney weekends and one half marathon near the end of my trip after my normal park touring before signing up for my first Dopey. By that point I already had a tried and true strategy of enjoying the parks while also taking in a lot of shows and/or sitting on a bench for 20-30 minutes as needed. Now if this is a rare trip, then you should consider that races will likely curtail your park time especially if the marathon is one of them.
I'm a back of the pack runner and this is about my norm:
5K: in the parks by 9:30am. Because they usually don't sweep the 5K, I have more time to stop during the 5K
10K: in the parks by 10:00am.
Half: in the parks by 11:30am.
Full: in the parks by 3:00pm.