No. That's not how that works. No one is allergic to coffee because they are allergic to cockroaches/chitin. People are allergic to coffee because they are allergic to coffee. Maybe you meant to say that there are people who can't drink coffee that is brewed from pre-ground beans that also have chitin/cockroaches in it?
Also this can be an acquired allergy. Some researchers who work with cockroaches acquire it. They can no longer drink coffee afterwards.
Otherwise it's exactly how it works. You're either stupid or misinformed. Go fix that.