For example, no provider would provide service under a bespoke contract obligating them to knowingly host & serve illegal content (because this creates legal liability for the provider).

What is alleged about Parler would likely fit into the instant-kill provisions of even any reasonable bespoke contract.

[Edit: obviously this does not apply to providers specifically in the business of catering to high-risk customers. Stripe doesn't do gambling or porn, but other providers presumably have different pricing or risk mitigation/tolerance and therefore on can use credit cards to pay for these items.]