Has there ever been a political tendency which have emerged independently of anarchism/marxism, but with similar content/ideas

Abolitionism in the US to a degree?

With slave revolts in the US, while slavery and wage labour are not the same, they are definite and immediate precursors to proletarian uprisings. There's also been (mostly) an historical erasure of maroon communities of escaped slaves.

This on Maroons in the Caribbean/US: https://libcom.org/library/dragon-hydra-historical-study-organizational-methods

Related to the above piece on Maroons:
https://libcom.org/library/silences-suppression-workers-self-emancipation-historical-problems-clr-jamess-interpreta

Both of these focusing on movements before anarchism/marxism were recognisable political ideologies, we're talking contemporary with the sans culottes in the French Revolution.

This on Reconstruction is interesting as well: https://libcom.org/library/w-e-b-du-bois-proletariat-black-reconstruction-ferruccio-gambino

I think you could probably argue there's an independent tendency there of movements against plantation slavery and colonialism which later had crossover with anarchism and marxism (and like both also developed out of the radical end of bourgeois liberalism). This usually gets lumped in Pan-Africanism, but Pan-Africanism covers a very broad range of ideologies and movements really.

Neo-Kantian "ethical socialism"?

Alemanism? Blanquism?

besides "ethical socialism", another minor current in the Netherlands, Germany, Switzerland and Scandinavia was religious socialism, deriving its theories out of a radicalization of 19th century Protestant liberal theology

Some millenarian religious movements that spurred peasant revolts could be considered anarchist-like: they demanded a radical restructuring of society and often wouldn't recognise earthly authorities.

In China, the Yellow Turban rebellion in 200 CE (Taoist) and the Taiping rebellion (Christian) in the mid-19th century come to mind.

They might not be recognised as 'political tendencies', but imagining mass political movements (like anarchism or Marxism) before capitalist modernity can be quite difficult anyway.

#8 showed me just what little i know of Chinese history

In religion, Anabaptism, Ubuntu and Primitive Methodism have aspects which could be considered socialist or anarchist (the latter provided a lot of directly socialist preachers in East Anglia in latter years). The Levellers, Ranters and Diggers as well in Britain, off and on.

In terms of traditions that developed totally independently:

• The Rotinonshón:ni ('Iroquois Confederacy') prior to colonial contact had independently developed ideas and organisational forms with some similarities to anarchism, such as common property, and communal self-government.
• Mbah and Igariwey argue that traditional (west) African village life has many traditions of stateless self-organisation informative to a contemporary African anarchism, as an alternative to 'African socialism' organised through post-colonial states.

It's tricky because many movements after 1870 or so would probably be at least aware of Marxism and/or anarchism and so not been totally independent. That said, there's a few that may be of interest:

• Most famously, Zapatismo synthesises Marxist and anarchist ideas with indigenous Maya traditions (you mention Mexico in the OP so this one might be obvious)
• Abahlali baseMjondolo have developed a distinctive movement based on direct action, class struggle, and anti-parliamentary politics. They grew out of the anti-Apartheid movement (and subsequent integration of the ANC into the capitalist state), and are certainly aware of Marxism and anarchism (holding study groups on them, iirc), but have forged a distinct kind of class politics.
• Mike mentioned pan-Africanism, one such group was ASCRIA in Guyana, which initially rejected Marxism for black nationalism, but in the course of post-independence strikes and land occupations came to adopt a class struggle politics with some echoes of anarchism (see Eusi Kwayana, The Bauxite Strike and the Old Politics)
• Ghadar, an Indian anticolonial movement. I'm only vaguely aware of them from Maia Ramnath's Decolonizing Anarchism, but she's written a separate book (which I haven't read) Haj to Utopia: How the Ghadar Movement Charted Global Radicalism and Attempted to Overthrow the British Empire which discusses their "seemingly contradictory ideas" and links to international anarchism.

in Burmese (Theravada) Buddhism, there were (albeit reformist-leaning) currents which interpreted the Nibbana as a kind of "heaven on earth", U Nu who was prime minister there around 1960 was influenced by these thoughts

I don't know if there's direct continuity, but the Black Consciousness Movement and Steve Biko are a precursor to Abahlali baseMjondolo https://libcom.org/library/year-fire-year-ash-soweto-revolt-roots-revolution has quite a bit about their influence on Soweto '76 (and it shows how the ANC was headed for integration into the state long before apartheid actually ended).

Just to say this is one of the most interesting books I've read for a while. Matthew Quest who wrote the introduction, also wrote this essay on CLR James, which partly goes into a re-reading of the Black Jacobins: https://libcom.org/library/silences-suppression-workers-self-emancipation-historical-problems-clr-jamess-interpreta

https://anarchyinaction.org/index.php?title=Zomia

?

Have to admit I've not actually read it all the way thru yet so can't say for sure, but "The Dragon & the Hydra: A Historical Study of Organizational Methods" might be relevant as well: https://theanarchistlibrary.org/library/russell-maroon-shoats-the-dragon-and-the-hydra

I linked it upthread and it definitely is, very strongly recommend that one.

One point CLR James makes in Black Jacobins was the very strong ideological and material relationship between the Haitian Revolution and the French Revolution, and support from the sans culottes for abolition.

So we can say not only did plantation revolts, maroonage and other resistance to capitalist (colonial, forced) labour systems develop independently of anarchism and marxism as ideologies, but also that the movements of workers in the colonies and the European working influenced each other. Even if only slightly, and even if this relationship isn't necessarily directly referenced by French and German authors in the 1830s-1840s and didn't result in much written theory from the protagonists (hard to write it down if you're illiterate of course).

On top of that news of slave revolts was massively repressed due to fear of them spreading, even locally in some cases, so a lot would have gone unheard of.

https://russellmaroonshoats.wordpress.com/2012/08/10/the-real-resistance-to-slavery-in-north-america/ on US Maroon communities, also by Shoatz, is also excellent. The Dismal Swamp and the Seminoles are fascinating.

Haven't read it yet, but I think Cedric Robinson's book deals with this:

https://libcom.org/library/black-marxism-making-black-radical-tradition-cedric-j-robinson

Would also recommend this very, very late Marx where he talks about the potential for the Russian Mir to go directly from communal peasant life to communism. It's slightly orthogonal to this discussion, but it shows that Marx had a much broader view of class struggle and the potential for the development of communism than later 'stage-ist' Marxists - and also that he massively revised his earlier chauvinist views of the Slavs.

https://www.marxists.org/archive/marx/works/1881/zasulich/index.htm

I get incredibly frustrated by books like Peter Marshall's History of Anarchism which spends a lot of time on random philosophers who didn't like authority trying to claim them as anarchist precursors.
But I think it's very fruitful to look at actual peasant, proto/early-proletarian struggles from say 1600-1850 which produced the militant, liberatory class struggle that anarchist and marxist writers built theory out of. We can also recognise that the contribution of colonised people to this has been under-theorised and historicised - don't have to blame Marx or Bakunin for that, but it's possible to correct some of this still with hindsight.

It's also not a problem only with history up until 1850, I recently did a load of reading around strikes in Africa from 1930-1960, most of which I'd never heard of until I went looking for them (written up here: https://libcom.org/blog/post-war-strike-wave-sub-saharan-africa-02032018). And discovered Makhan Singh, who translated vol 1 of Capital, but had never heard of until last year: https://libcom.org/library/singh-makhan-1913-1973

Side note: amazed we got this far and no-one mentioned pirates yet: https://libcom.org/library/many-headed-hydra-peter-linebaugh-marcus-rediker

On this, Susan Buck-Morss' Hegel, Haiti, and Universal History makes a persuasive case that Hegel was hugely influenced by the Haitian revolution. Obv Hegel in turn was a huge influence on Marx(ism).

Damn I've seen a lot of people asking about connections from Haiti -> Marx but had never come across this, thanks!