In the US it's illegal to require a degree for almost all postitions that people around here are concerned with. Companies always try to elide this, but bizdev, marketing, programming, sysadminning, sales, and starting a company are not classified as the kinds of skilled positions for which a diploma can be required, such as engineering, finance, architecture, law, medicine, etc. I don't know if this maps perfectly to board-certified professions (IANAHR), but there does appear to be a pattern.
Illegal? Most employment in the US is at-will. You can hire or fire for any reason or none at all, as long as you're not selecting based on race, sex, religion, etc.
Where is it illegal to require a degree in Marketing for a job in Marketing?
There's legal notions that state you can't create arbitrary requirements. i.e. take a job where employees are on the phone with customers all day, it turns out that entrepreneurs would rather want your name to be John than Juan, Kwame or Mohammed. And given racial differences in socioeconomic standing, which create differences in educational attainment, it's easy to say a college degree is a requirement for the job, when you're really just using it as a proxy to hire a certain ethnic profile.
This is just an example, I'm not claiming here it's widespread (although it wouldn't surprise me in some industries, and many blind tests have shown preferences, but that's besides the point.)
Now this isn't new, so there have been court cases in the past. And they shaped a precedent which loosely states that you can't just say you need a degree for the job. You need to back that up with real data. This isn't common practice, but it's the law. So for a job where you need to do rudimentary work, there's technically quite a high burden of proof on the employer to require a degree for that.
The famous case is Griggs vs Duke Power Co[0][1]
There've been more cases since, it's not that hard to find. In any case, no it's not broadly illegal to ask for a degree at all. But there is precedent that unnecessary tests, e.g. a degree requirement for a telemarketing job, are indeed illegal.
I wouldn't know for certain how a judge would rule on the examples given by the person you replied to, like system admin or marketing, but I suspect the notion a degree would be required would be found entirely reasonable by a judge, like syst admin or marketing. But I get his point. I've got friends who work e.g. as a credit analyst, which is a job they say they and their peers could've done at age 16 without even finishing HS, yet it's a typical job that requires a degree and that a judge would probably be convinced of that it requires a degree.