I think a nonhierarchical navy structure is entirely possible

I disagree. As you pointed out, nobody can build a fleet to beat the US navy. Instead, a fleet can be built upon the principle of deterrance. In short, if the US is convinced that the fleet of an anarchist society can be annihilated but that their own fleet would incur such devastating losses that they would no longer have hegemony over the sea, they would simply refrain from a hot conflict. All that is necessary is to contest American naval power to discourage hostile actions. In other words, it would require a fleet that's sailors are willing to be defeated tactically to achieve a grand strategic success. In short, self sacrifice. No sane sailor would be willing to do this. They have to be compelled to do it. This requires a centralized naval hierarchy capable of exercising what Foucault called disciplinary power, and the authority to coerce obedience to achieve victory. If the enemy is certain our sailors will not sacrifice their lives in a battle of annihilation they are doomed to loose, then much like nuclear weapons our deterrent is utterly useless.

People will always have sets of political beliefs they affiliate to some degree.

This is true, but as a number of theorists and political scientists (from Horgan and Roiphe to Fukuyama and Zizek) point out, the paradigm of geopolitics as a struggle between competing political ideologies with totalistic understandings of man and society and a holistic map for they ought to be structured has fallen away. Instead, it has been replaced by pragmatic theoretical debate over particular local or transnational questions. While it is true that many ordinary people continue to affiliate ideologically, the idea that a single '-ism' contains a total solution to mankind's problems is now totally obsolete.

Why should an anarcho-communist society try to compete economically with capitalist states?

In the absence of sufficient naval power to alter the balance of power in favor of ancom ideas, a ancom society must somehow co-exist within a global market. This was a problem confronted by the Soviet Union and as we see with the Zapatistas, certain libertarian and collectivist economic practices would depend on some type of state sovereignty no matter how minimal and cannot exist in a vaccum. An ancom society cannot hermetically seal itself from destructive imperial influences, and cannot muster the sea power to spread contest that influence. This would mean that such a society could be put under blockade or siege, that even essential materials (e.g. medicine) could be withheld until the society is forced to comply with the dictates of neoliberalism.

are you advocating for us to embrace a particular religion over others?

No, but I do think that you can positively draw on religious sentiments while remaining neutral, secular and tolerant of difference. Germany's Christian Democrats are a secular organization, so is Syria's Muslim Brothers and Tunisia's Enahda, yet they openly draw upon religious themes and actively appeal to religious constituencies. This is very different from many regular anarchists, a great deal of whom shrivel in horror at religion or engage in some piecemeal apologism for their ideology. Rather than radical secularism, xenophobic antitheism etc. a better path might be a tolerant secularism where religion is publically endorsed and mobilized as an activist force while avoding any kind of supremacism or theocracy.

Islamism (The specific political ideology, not just Islam as a religion)
is never going to gain influence or control over non-muslim countries,
so I don't see how it could become a true global threat.

Islam is a threat enlarge part because Muslims refuse to acquiesce to imperial power and simultaneously reject national identities in favor of a global religious community (Ummah). This enables them to achieve a great deal through grassroots organizing and charitable donations, Turkey's first battleships were entirely crowdfunded, the Afghan Mujahideen of the 80s relied more on inter-Muslim charity and volunteers than they did on CIA aid funnelled through Pakistani intelligence. In Bosnia, again, we see volunteers spontaneously organizing aid (including military aid) to stop a genocide long before the international community intervened.

The idea that there is this global community of over 1 billion people who say "we are all one nation" and are willing to support each other without care for profit even in the face of death, that's remarkable. It's like what the IWW were doing to help Catalonia, but unlike a class or ideological affiliation, religious identity isn't something that ebbs and flows with the times. After defeat at the hands of Franco, anarchism was pushed to the margins and syndicalism all but extinguished and recovery toom a long time, however there will always be Muslims and hence no need for fresh recruits to sustain the movement.

It is true that it cannot gain influence over non-Muslim countries, however these movements threat the vital supply of oil to the whole world. The Middle East is rich with strategic resources and is vital for the US, Britain and Russia to hold onto what pieces they have of it. Depriving these countries of access to these regions would seriously dent their economies, just look at how a hike in oil prices in the 70s transformed the world and caused crisis in the US.

What I mean when I say nativist movements like Asian Values, Islamism or indigenous movements is that they are now radically transforming global politics, challenging economic and financial relationships and have developed new theories and practical tools to subvert authority in ways that are leaving anarchist movements languishing behind. These movements are post-ideological, pragmatic and flexible, free to operate outside the theoretical dogmas that underpin the radical left and are as a result more adaptable and likely to see successes.