It's not about the relationship between the end user and the broker, it's about the relationship between the broker and the clearing house. Trades take two days to settle, and the brokerage needs to post collateral with the clearing house to reassure them that they have enough funds to settle the trades. When volatility goes up, clearing houses demand more collateral to allow further trading, which the brokerage might be unwilling or unable to provide. This is independent of whether the end user is using margin.
Well, in a world where users had to have fully funded their accounts before making any orders, the clearinghouse would have nothing to worry about. So it's not exactly independent from whether end users are using margin.
It looks like RH let hordes of new users onto the platform and allowed them to put in GME orders before having those users' cash in the bank. Now the clearinghouse sees the volatility, throws up its hands and goes "listen RH, no more of these crazy GME orders from you until you have the cash to pay for them". Understandable – but that should be RH's problem, not that of its users.
What's not OK is RH's sledgehammer solution of disabling buying for all users, even those whose accounts are fully funded, not to mention force-selling people's shares against their will. IMHO they deserve all of the anger and lawsuits currently directed at them. (Edit: unless, of course, they are only force-selling stocks that were bought on margin in the first place, and if their T&C let them do that, in which case ¯\_(ツ)_/¯)
The clearing house doesn't know who is trading on margin and who isn't. They don't have visibility into the brokerage's interactions with their clients. They can't "only allow trading for non-margin accounts".
No, but RH knows, and could make that distinction if they wanted to. RH is punishing margin and non-margin users alike until it has enough cash again to resume making orders.
To be clear, the RH T&C very broadly protect them in case of any arbitrary service interruption, so on paper they're probably entitled to do whatever they want. But at the end of the day, it was them who got caught with their pants down because they went too far in their UX/risk tradeoff, and now users are paying the price and are understandably pissed.