Maybe if it were Roku, it would. They are the ones picking fights with everyone. The apps is there, and it works. I just tested it myself. Here is photographic evidence from one of my Firesticks just now which was installed directly from the Amazon App store:
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This isn't a political problem, but rather a technical one.
I don't know how many times in my experience one app has worked on one platform but not on another over the years, but it is significant. I used to have this exact problem with Netflix for years. I even have problems with Prime Video maintaining UHD resolution on the Firestick 4K that I don't on other platforms to this day, and I have a gig internet connection. For whatever reason, this happens. A company like Amazon isn't going to block a service that is making them money unless they detect something illegal or directly harmful happening on that service which is in violation of their terms of service. Whether you agree with the politics of Newsmax or not, they are doing neither of those things.