Should people with hemophilia avoid aspirin?  

Yes. Hemophilia predisposes to bleeding due to lack of blood clotting factor. Asprin and nsaids such as Motrin can increase bleeding risk and should be avoided. It is best to consult your treating doctor for your unique situation.
Hemophilia & aspirin. In general, it is recommended that patients with hemophilia avoid Aspirin and similar compounds such as ibuprofen, naproxen, and indomethacin. The only over-the-counter pain reliever not associated with excessive bleeding is acetaminophen.