Both sides of that case agreed that the company was choosing to deny its custom wedding cake services to a gay wedding because of the owner's religious beliefs against gay weddings, not because of anyone's speech. In other words, they objected to making a wedding cake because of attributes inherent to who the engaged couple were, not anything that was being said or expressed.
I view it as plenty consistent to forbid businesses which serve the public from choosing not to serve customers based on innate aspects of who they are, like being the same sex or gender as each other, while still allowing them to make such choices in reaction to the customer's speech. Sometimes the line is clear (no speech was at issue in this case), and sometimes it's blurry, but that's absolutely a consistent rule whether or not it's the one you support.
The reason the Supreme Court ruled for the bakeshop was very narrow. The ruling acknowledged that states can constitutionally have non-discrimination laws that apply neutrally to businesses without making available exemptions due to religious beliefs. The ruling was just about the behavior of the Colorado Civil Rights Commission in applying their state law to this case, which the Supreme Court majority viewers as hostile to the owner's religious beliefs and not religiously neutral as the government must be. So it was about religious bias in the government action, only. One member of the 5-4 majority wrote that he might well have ruled the other way had the commission acted neutrally.
The concern expressed by the cakeshop was primarily about making a custom wedding cake for a gay wedding, not the message. Put differently, they wouldn't have made a custom cake for this particular wedding, knowing it was a gay wedding, even if there were no message requested. The ruling was not on free speech grounds.
Anyway, the cakeshop scenario is a bit different in another way: it can be argued to involve expressive activity on the part of the employees who create the custom cake, since it's far more artistic than mechanical, and since they do literally write any requested message with decoration. By contrast, Discord's actions against the customer are simply a choice of which speech by others they choose to allow to flow through the platform they control, plus a statement of their own speech which they choose to put out about their action.
(For what it's worth, they've chosen to partially reverse their ban since we started out discussion, if I understand right.)
If you want to ensure there is a content neutral platform, maybe the best way (at least under US free speech concepts) is to advocate for a government-owned/run Internet group communication platform, just like we have in offline life when you go to the nearby park or plaza to protest, or when you send mail to everyone in your local community through USPS.
Everyone agrees that, in the US, the government can't constitutionally censor that on the basis of content or viewpoint, with a few exceptions such as forbidding child pornography. I'm guessing that platform wouldn't keep getting funding from the politicians if it got too much offensive content, but if it wasn't shut down entirely, they couldn't be selective about which speech to permit.
The problem with modern leftism is consistency in beliefs. It's why I had to just walk away despite still agreeing with most leftist policy ideas.