What's an "exit plan" in the context of small personal non-corporate projects?

It depends on what commitments you made to your users. It could be as simple as just abandoning the project or it could be something more elaborate like handing it over to someone else.

But why do you have to think about this "as soon as you have your first user"? Not every project is a business and not every project needs an "exit plan". Not everyone doing a project needs to think in entrepreneur terms.

The “exit plan” could be as simple as “do nothing and abandon it”. You don’t “have to” do anything and are under no obligation to do anything, however decency says that in some circumstances you probably should.

When you have people using your stuff, you have to decide whether you care about them or not. It’s ok not to care, you don’t owe anybody anything, but if you lead them on or give them the impression that you do, then they are invested in something because of it and it would be pretty shitty to just disappear. You still can, if you like, but you should at least do it consciously.

If you have people the impression that you would support something then you need to be clear with them that this isn’t actually the case, otherwise you’re a bit of a dick for leading them on. It’s perfectly ok to just throw something out to the world without supporting it in any way and it’s also ok to step back from something you did once support, but you should at least communicate this so people don’t get the wrong impression.

If people are interested in your project, it's courteous to let them know what's going on, even if just to tell them the project won't continue.

I fully agree. I'm just questioning the use of entrepreneurial terms such as "exit strategy", especially early in the life of your project.

    "What are you doing?"
    "I'm painting, some people bought my pictures"
    "So what's your exit strategy?"

The terminology doesn’t matter. It’s used here because this is a very entrepreneurial audience and most people understand what is meant by it. I don’t think anyone means to imply that you need to treat your hobby/side projects like a business.

Well, the terminology matters to me. The language we use tends to frame how we think about issues. I find the language of entrepreneurship distasteful when used outside a business context.