This is bananas. I'm a cancer survivor and I've administered hundreds of job interviews; I guarantee a large part of the difference in callbacks, if not the whole difference, is down to the combination of resumes and hats. Explaining a gap on your resume, great. Wearing a hat with "CANCER SURVIVOR" on it to an interview, ok, a little unusual, but whatever. Doing both? That's weird—not because it has anything to do with cancer, but because the applicant is putting so much energy into driving home an irrelevant point. I'd feel the same way if you explained a gap by saying you volunteered at a sloth rescue in South America (which would be awesome) and wore a hat with "SLOTH VOLUNTEER" on it (which, combined with the gap explanation, would be a bit much). It just screams "I have no idea who I am so I've constructed a fragile identity around this one aspect of my life."