Are people with apple allergies allergic to baked apple foods?

May not be. People with the form of apple allergy that causes mouth and throat itching, so called oral allergy, or pollen fruit oral allergy syndrome, is usually a cross reactivity with pollen allergies, and is usually due to a heat labile protein. Heating destroys the protein's effect.
Some but not all. If when eating raw apple only your mouth itches & your throat feels tight you may have oral allergy syndrome caused by a allergy to birch pollen. If you also have upset stomach, vomiting, coughing, difficulty breathing, hives, lip swelling, or dizziness you likely have true apple allergy. People with the latter have the same symptoms with baked apple. Skin or blood testing can differentiate the two.
Test. Now it is easy to test for food allergies. Request food allergy testing from your doctor. Many food allergies are false positive.