In my experience this decision comes down to two factors: competence versus conformance. If you want to hire somebody good you will look for someone self taught who does this for a hobby on various side projects. Being good at this meant a solid understanding of how web technologies work with a solid foundation in both theory and practice and none of that was taught by universities. Specific examples include: lexical scope, tree model navigation, accessibility, functional programming, asynchronous programming, and so forth. Early on I learned a lot about these concepts reading unrelated books about XML. I didn’t any of these skills coming out of my university educated Java developer peers, which for those guys life was limited to OOP and SQL only.
If the goal is to put a body in a seat as rapidly as possible then you will look for somebody with a CS degree and remove competency as a factor as much as possible, which typically means double and triple down on large frameworks and third party tools. The goal is to ship features, not solve problems. I don’t want to be a nothing script kiddy, so as a JavaScript developer I am less employable.
In general employers look for people who have relevant experience and the skills they think they need for the job. A degree communicates some level of study and practice in an environment that probably included teamwork and following instructions. If you teach yourself you have to prove you have the programming skills, and that you can work with a team and understand the business domain well enough to add value.
To answer your question, an employer will hire a self-taught programmer if they think the programmer can do the job. I don't think the self-taught part causes skepticism, it's more the lack of experience in a business and team environment. A degree isn't a real track record of accomplishment but it's usually accepted as a proxy.
I taught myself programming and got a job after a few years of study and practice (mostly while I was in high school and college). I got a job and never finished my degree. That was a long time ago (more than 40 years ago), and back then employers would more frequently hire people they expected to train and mentor. That doesn't seem to happen much these days, everyone has to prove they can fit in and produce right away.
40 years ago, very likely, your salary would have been a "normal" one, and your employer would have had less hurry in having you productive, letting you some more time to learn/adapt/etc. and - as well very likely - your attitude towards the employer would have been different from the one I see common today (let's work here for max 2 years then find another job) and - viceversa - you were likely seen as a resource on which it was worth to invest some time and money in the long run (as opposed to an expendable -and possibly micro-managed - employee that can be repolaced any time).
The market has simply changed, not only in computer tech/programming, firms expect that the candidate is "ready" and use (as you say accepted as proxy) degrees and quick technical interviews to justify the choice (of hiring or not hiring you).
My first job was with Nike, junior programmer brought on as a contractor with a big crowd of other young programmers looking to get training and experience. We got access to training and assigned two mentors. After two months we either got offered full-time jobs or let go. IT/software development didn't exist as a separate division in big companies back then. I worked in inventory/logistics, so I learned a lot about that business domain along with the programming stuff (DECSystem 20 BASIC, Fortran, COBOL, assembly language). That was a great opportunity to launch my career, and I met some great people there. Decades later one of my former Nike mentors hired me at a software company he had started up.
I've worked in the software business for over 40 years and I don't think I have ever applied for a job. I always got hired because I knew someone, or someone knew me. Contacts and friends always worked best. I got a couple of jobs through recruiters but in both cases I had contacts inside the company.
The greatest singular advantage I would give those of formal education is regarding their presumed reading and comprehension levels, as well as demonstrated minimum competence in following instructions and completing assignments.
With a few specialized exceptions formal education does not competently prepare candidates for general application development. Their methods, stacks, and habits will come by the example given by the existing team.
Disclaimer: I am a self taught developer with over ten years experience who has functioned as a hiring manager (hiring dozens of developers and engineers over the years.)
If it’s no degree, I assume a common first question would be “why?”. But provable coding chops and positive personality traits should mitigate that question. Hackers still exist - it’s not taught as much as learned.
Yeah, maybe it's not the missing degree bud.