Users are allowed to put what they want in their user profiles, within reason.
Generally speaking, users are allowed to put whatever the heck they want in their user profile. This includes links, images, text... as long as they stick with two guidelines: It should be SFW, and has to be non-offensive to people.
This means: No naked pictures, but a picture of their kid is fine. No links to porn sites, but a link to a site that promotes non-mainstream science? Fine. The user profile reflects on the one who wrote it, not the site as a whole. What you put in your user profile reflects on you.
I'd advise checking out this Meta.SE post, which explains what is acceptable for user profiles, generally. To sum it up, I'll take the first two bullet points:
Generally speaking, your "about me" is just that—what you want to share with the world, and we try to allow users a good bit of freedom there.
However, in the rare cases where what's there is likely to be truly offensive to large groups of seemingly reasonable people, we may not allow it.
And this handy image guide:
So, you state:
These people even have thousands of points of reputation, but the minute you check their profile, you're baited to go to "CrackpotLandia" (such as academia.org).
That's perfectly fine. You don't choose to put that stuff in your profile; that's fine. But it's perfectly within the rules to put links to your work in your profile - there's even a special field for including a link to your site.
Also, may I point out that calling people 'crackpots' may be a violation of 'Be Nice'? I'd advise always sticking with this line from the chat FAQ (emphasis added):
We expect community members to treat each other with respect … even when they don't deserve it.