maybe it's just me that always has that "under penalty of perjury" sarcastically running in my inner voice whenever I see these types of ridiculous EULA type of things.

Somebody should really force the issue to "have standing" to fight the ridiculousness. I'm shocked WP Engine hasn't already

Companies are absolutely allowed to arbitrarily ban certain people or groups of people from using their services, and if you sign a contract attesting to you being allowed to use the service, you can absolutely be found guilty and/or liable of breach of contract.

Illegal? Or just a civil problem? Illegal takes it in a pretty severe direction.

Some courts have interpreted the definition of "unauthorized access" in the CFAA pretty broadly. That checkbox about WP Engine is arguably an "access control mechanism" since you can't access the site without checking it. Maybe it's a stretch but it's not that much of a stretch.

I could see a breach of contract argument too.

IANAL.

IANAL either but I was under the impression that changed with the Van Buren v United States Supreme Court case [1]. If you register and accept a EULA, it’s no longer “unauthorized” access, regardless of whether you exceed EULA limits, as long as you’re using the authorized interface (as opposed to trying to get access to the servers via SSH or some other side channel). It’s not the criminal courts’ job to enforce access limits.

[1] https://www.law.cornell.edu/supct/cert/19-783

IANAL, not from the US either. But if you register, you are signing a legally-binding licence agreement. Doesn't lying or giving false information nullify this contract?

For example, if you register on wordpress.org while claiming you have no affiliation with WPE, but you did have any sort of affiliation, they could consider the contract null/void, and claim the access was unauthorised because the contract wasn't valid.

The contract can be null and void but if you can still login, it’s not unauthorized access. The burden is on the company to pursue breach of contract. That’s my reading of the decision but again, IANAL.

Civil infractions are still called "illegal", at least in the US

It is not illegal to beach a contract. You can be held liable for damages but there is no criminal penalty and some judges think beaching contracts can be good (so called efficient breach)

It is legally enforceable i.e. it is not something you should just say “well it’s not an agreement with the government so I can breach!”