GNU, and FOSS in general, is neither capitalistic nor communistic. It is academic.
It works in exactly the same manner that Western academia has for much of its recent existence, in which discoveries are published, shared, collaborated on, and built on, albeit at a pace much accelerated by the ability to collaborate in real-time over the Internet, instead of having to wait for the publication of monthly journal articles and expensive lab experimentations (like the LHC).
Just because the people involved in FOSS are not doing this directly for money does not mean they're giving away the fruit of their labor for free, or being coerced as Soviet Communism was known for. While creating things that directly improve their own lives (scratching their own itches), they also gain the opportunity to spend their lives living their passion doing stimulating work, gain recognition amongst a group of peers spread all around the world, become known as experts in their field (leading to paying gigs from commercial outfits), and create things with the potential to advance the human race and make the world a better place. All of it 100% voluntarily, uncoerced. If that's not Life, Liberty, and the Pursuit of Happiness, I don't know what is.
Go reread what Ayn Rand says about trading value for value. Whether you're trading the fruits of your labor and talent for money, or for something else of value to you, either fits just fine with her philosophy. Ultimately, she was an advocate for the creation and fair exchange of value and real wealth, of which money is just a store, and without coercion. There is absolutely nothing about FOSS that is incompatible with her beliefs.
This is one of the biggest problems with the Conservative movement these days, a misunderstanding and misapplication of their own ideology. Too many seem to have merely a superficial understanding of it, a worldview that if corporations, direct profit motive, and consistent % improvements in quarterly statements aren't the driving force behind something then it can only be the antithesis of Truth, Justice, and the American Way. Be it FOSS, Net Neutrality, movements to reduce corporate spending in politics, if corporations are against it or orthogonal to it, then it must be anti-American.
Einstein once advised that 'everything should be made as simple as possible, but no simpler.' I think the right would do well to reconsider their world view with that in mind.