> Would allowing only minorities to work on their vehicles at home solve the problem?
This is a strawman - nobody is asking for this!
> why would race need to be brought into the equation when it's so much easier to communicate about the core issue rather than discuss things in the context of a more complex issue of race and equality?
Let's look at literacy tests for voters. These are similar as you can absolutely construct a plausible argument for them that never mentions race at all - "We just want to make sure that people voting actually understand what they're voting for". And there were likely advocates for these laws who believed that! And literacy tests of course affected more than just African Americans. But - the near universal consensus among historians was that the primary intent was to suppress black votes.
Not discussing race when discussing voter literacy tests is avoiding the crux of the actual issue. If you only engage with voter tests on the "actually understand what they're voting for" level you're avoiding the much more important conversation of whether this law is passed in good faith.
> The likelihood that it disproportionately hurts members of a certain race wouldn't matter if the issue was solved in a way that benefits everyone.
And therein lies the rub - how can it be solved in a way that benefits everyone? If there was a universal benefit solution for every problem politics would be easy! In the case of literacy tests there is no such solution - there was nothing that you could give the advocates for suppression policies that would make them happy that wouldn't come at the expense of minorities. In this case? Hard to say, but I really doubt there's an amicable solution.