Just my opinion but the two resorts you are listing would be on my list to avoid. My daughter has several food allergies (peanuts, tree nuts, eggs, bananas and soy protein). Although gluten is not an issue for her, we do have some experience with food allergies at WDW resorts. We are also a family that likes to eat several CS meals at our resort so it is important to us.
Beach/Yacht Club and Boardwalk are difficult because they do not have a traditional CS for breakfast. BC/YC has the Marketplace but the menu is extremely limited and when we were there, the food was made in another kitchen and basically ready-to-go under hotlamps. Unless this has changed, it would be difficult to get something special prepared. Boardwalk has the BW Bakery but items there are very gluten heavy, IMO.
CSR was a different issue for us. We found a lack of understanding/urgency/language barrier .....not sure how to categorize....with our daughter's food allergies. It is important to know that the food service at CSR is not owned by Disney. This resort food service is run by a different company(I believe they also run the restaurants in the Mexican pavilion at Epcot as well) Even after emailing the chef contact at the company AND a face-to-face with the chef on our first night at the Pepper Market, my daughter was served food that she was allergic. They basically lied or didn't care?. I was told there were no egg noodles in their kitchen so the pasta station would always have egg free noodles. On our last night, she was served pasta that looked like wide egg noodles. After asking the station server several times about the noodles, I was assured they were not egg noodles. Upon reaching our table, I could not get past the look and tried them, they were indeed egg noodles. I took the plate back and asked to speak to the manager/chef on duty. I was then told, yes, they were egg noodles, sorry. Yep. That was it. Just sorry. Thank goodness I did not let her eat them. Their indifference was appalling. Didn't help that I ended up with food poisoning that night from something I had eaten at the PM.
I would suggest staying at a resort in the MK area. Each resort has traditional CS in the hotel with trained CMs who do a great job with food allergies. We have personal experience at Poly but will be staying at GF this summer. It is great that they are connected by monorail/boat for easy access as well to increase your resort CS options without a lot of hassle.