Minimalism is about having what is essential to a fulfill a certain need or goal. What is essential varies from person to person and of course is vastly different whatever we are talking about a software engineer living in a city apartment vs. a farmer.
So I see minimalism being about prioritization. During "normal" circumstances it is pretty much purely voluntary, but the more self reliant you want to be, the more it becomes a necessity. With limited resources you have to prioritize what tools, skills and materials you acquire in what order, quality and quantity. You end up with good enough, minimal solutions for a lot of the problems.
My farmer grand parents where 10x the minimalists I ever was in my view. But for them, it was just how they grew up, not a lifestyle choice about aesthetics.
This is what I mean by poverty. Most people who are ingenious live a balance of self reliance, minimalism (usually due to lack of money) and poverty.
By poverty I do not mean that taking one step into self reliance makes you instantly impoverished but it frequently means doing without some luxury or need fullfiled that people are accustomed to. It usually comes in the form of "making do".
Are you trying to be a homesteader, entirely off-grid and not reliant on society? Or are you trying to be financially self-reliant, not relying on a paycheck? Or are you trying to be personally less reliant on things and items? These are all different ideas that get wrapped up into this conversation, and like the OP said, they're not all compatible.
If you want to be an off-grid homesteader, you're going to need a lot of tools, materials and skills. If you want to be less reliant on things, then you are going to have to be content with being able to do less.
None of those things are bad, but the conversation is incomplete if we don't make clear what we're really talking about when we talking about self-reliance and minimalism.