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FWIW, I'm on an MVNO of Tmobile, and I can reach lichess.org but not lichess.com.

I can't reach lichess.com on my home internet either (Service Electric, a subsidiary of PennTeleData, IIRC)

That’s unrelated. The issue here is that SMS messages containing particular links are blocked, not that the sites themselves are blocked.

I believe they are blocking links to the websites in an SMS message.