Well, as you yourself have pointed out, several Americans have married into royalty, and to be honest, I have to say I really don't see what makes Americans less worthy than others to become consorts. In my opinion, Princess Grace made an excellent consort in Monaco, far better than many of her predecessors, nor did she come from a particularly upper-class background - while her father was rich, they were definitely new money.
Also, just thought I might point out that while they aren't American, the majority of the royal consorts today were born commoners, many not in the country in which they will someday be queen: Crown Princess Mary (born Donaldson, Australia) of Denmark, Crown Princess Mette Marit (born Haraldson) of Norway, Princess Maxima (born Zorreguieta, Argentina) of the Netherlands, The Princess of Asturias (born Letizia Ortiz). For that matter, every consort in the British royal family in recent memory has been born a commoner with the sole exceptions of the Duke of Edinburgh and Princess Marina of Kent. The Queen Mum, Diana, Sophie, Sarah Ferguson, the Duchess of Cornwall, the Duchess of Kent, the Duchess of Gloucester and Princess Michael were all born commoners, and yet (while some did not turn out so well) certainly the Queen Mum and the Duchesses of Kent and Gloucester are renowned for their work as royals and have been tremendously successful consorts.
Interestingly, it is some of the royal born princesses who are somewhat less succesful - for instance, both Stephanie and Caroline of Monaco have embroiled their principality and long suffereing father in contraversy and embarrassment.
As to your question, yes, Harry would forfeit his right to the throne if he were to marry a Catholic, American or otherwise. However, he could marry a woman who later converted to Catholicism without losing his place in the succession (as in the case of the Duke of Kent).
And just a note - people don't say Papist anymore - it's offensive.