Hamas, Palestine's most prominent Islamic political organization/military force, has recently produced its first feature film and I couldn't care less.
"Emad Akel" is an action movie about the titular commander of the Hamas military wing who was killed in 1993. He was Israel's #1 most wanted man after his suspected killings of 11 Israeli soldiers, an Israeli civilian and four Palestinian informers. An incendiary subject, to be sure.

So why don't I - a patriotic American - feel threatened by this development?

Mainly because I've seen Hamas-produced material before and it's all been crap.
There are numerous clips from Hamas-produced TV shows on YouTube. The most vivid example of one that comes to mind features a Palestinian Mickey Mouse lookalike being murdered by a greedy Israeli.
Sounds terribly offensive, and it would have been if I could talk it seriously, but the production values - from acting to screenplay to you-name-it - were so damn pathetic.
Hamas has already won the hearts and minds of many average Palestinians with its propaganda. If the quality of "Emad Akel" and other "Hamaswood" is on par with its past TV productions, I don't think we'll have to worry about the organization getting any new recognition from Palestinian intelligentsia or foreign film industries.