Religious Groups

Dodecatheon - Homophobia. They don’t allow same-gender marriage and don’t let gay people be priests or priestesses, as Timothy Jay Alexander says (and defends). They are also obsessed with swastikas and the ‘roman salute’ which is a white nationalist tactic.
YSEE (Supreme Council of Ethnic Hellenes) - Homophobia, xenophobia, and anti-Indigenous racism. They don’t perform same-gender marriage. It’s in their FAQ and their justification is bullshit too. Here is an elaboration on their refusal to officiate same-gender marriage, employing the ‘slippery-slope’ fallacy so typical of the worst part of monotheists they despise. Here’s an excerpt: If we change even once our ritualistic Tradition then there will be no Tradition (ritualistic, I repeat!) at all, because then we’ll have to perform marriage ritual also for a polygamist with 5 brides, also for a nudist couple that may want to be blessed nude, also for a BDSM couple that may want the one part collared, and so on.
They are also nationalistic and deeply antisemitic, making some islamophobic statements at times too.
Church of Hellenes -  extremists. They literally advocate for the use of violence to make Hellenismos a national religion. Delusional as fuck.
Elaion - Falls into a lot of the same traps of ahistoric anti-”monotheism” rhetoric as well as nationalistic usage of “Dodekatheism”. Most importantly, the moderators were quite late to kick racists in response to BLM (2020) and Elani Temperance admitted that bigots who were quiet about their beliefs would be allowed to stay. More on that here and here.
Hellenion - Thinks Heterophobia is real. Their bylaws are a bunch of horseshit. Islamophobia and anti-Semitism in the guise of anti-monotheism. Run by an anti-Vaxxer literally named Karen. Ableism so bad that multiple board members quit in protest.
Ellinais/A.E.T.H. - Xenophobia (translated article here). Deeply and violently anti-immigrant. Nationalist and anti-Turkish articles by PR officer Leonidas L. Billis.
Ἑλληνικὴ Θρησκεία τοῦ Δωδεκαθέου/Hellenic Religion of Dodecatheon - may or may not be the same as Dodecatheon. Pushes antisemitic and Islamophobic conspiracy theories.
LABRYS - folkists paraphrasing Mussolini and creepy to young girls.

Online Discussion Groups and Websites

Pagans and Witches Amino - not necessarily Greek only, but I include it here because it’s pretty sizeable (enough to have its own independent app for a while on iOS). The mods are kind of corrupted, promoting newer mods over older ones with more experience, cultural appropriation is tolerated if not encouraged, and misinformation is rampant. A lot of people who are unable to distinguish UPG from historical sources and get angry if you point it out, as well as a lot of kids who think they are dating a god. Just...a mess, and toxic. I used to help run a chat and the chat was taken from us by mods without warning, likely because they didn’t like how we tried to get people to acknowledge when things were UPG or made-up. It’s hard to include receipts without implicating my friends who used to be there as well (it’ll end up just being receipts on individual users instead), so if you wish to see what I’m talking about you can take a look, but it’s honestly very corrupt and on its way out, IMO.
r/Hellenism, HellenicFaith and HellenicFaith.com - Run by Klaytonos AKA u/AzoresHeliokles on Reddit who literally worships an emperor of the Roman Empire (a violent and colonizing force).

HellenicGods.org - ahistorical nonsense about how ancient Greek religion survived. Compares anti-Indigenous violence with the usage of the word “pagan”.