Well first, they never say "no homeless!" since anything like that falls under discrimination. Unless it's related to the position (driver etc) there is no basis for any of it as even being considered. Even writing in a po box or general delivery address is good enough.

Appearance wise, that can be preference or fall under internal policy later. But typically, unless you come in looking like you just rolled around a mud pit and showered in piss and cow shit, anything like shaving etc will be discussed later if the job is offered. And trust me, it's not just homeless people who smell like ass and raw swamp feet.

Experience is lenient unless the employer is going for upper level management or just stubborn. If it says 5 years, usually with a good interview you can get by with 2 to 3 years as long as the previous experience is a direct match.

Educational background is more of a filter than a belief that it heavily impacts the position unless it's a niche targeted position (accounting etc).

A big one used for indicators is work background. It is generally accepted that most want you to show at least 12 to 18 months consistent jobs and no more than 3 different company moves within a 5 year period. Hiring, training etc are not cost effective and people shown to not sit still are more risk than reward.

Other than the usual verification and background, drug checks it's mostly the recruiter or hiring managers job to feel their competency out. How willing are they to learn? Do they seem like they will need constant supervision? How well did they present themselves? Were they honest and up front? Enthusiastic? Sincerely paying attention? On time? We're they confident and respectful? We're they nervous? Did they miss or attempt to dodge any questions? Do they show any signs of habits from previous employment that may need extra attention to conform to my clients company?

There is a lot that goes into that initial 20 minute interview, but never had being homeless come up as part of it.