I think a lot of people get caught up in viewing things through their own cultural lense and biases. You have to remember, to middle eastern countries such as Saudi, they view the practices we see as despicable as just and par for the course. The concept of sports washing would imply that they feel guilty or ashamed of their practices and were trying to cover it up through smoke and mirrors involving sport. In reality they seem to view the west's approach to criminals and dissidents as strange and unusual. I'm not defending the policies of the House of Saud here at all, far from it, but I find when dealing with international cultural understanding and politics it's easy to assess the situation through the lense of your own culture and sensibilities.
The Muslim religion has existed since the 7th century and the Arabic and Berber culture even longer, and is very explicit about how to govern the population and how morals and ethics should be adhered to. Unlike Christianity which has been seen as malleable and open to interpretation with major reforms coming through the protestant reformation and later the Vatican 2 reforms, Islam is seen as absolute and unchanging by its scholars.
Again I am not defending this and also at the same time I'm also not going to judge. It is what it is and many studies and surveys have shown that an overwhelming majority of Muslims like it as it is (Pew have done multiple exhaustive worldwide surveys with gigantic sample sizes https://www.pewresearch.org/religion/2013/04/30/the-worlds-muslims-religion-politics-society-overview/). As an English man (yes I see myself as such, we still live in the empire here, and I was raised by an English mother), I'm cautious about forcing beliefs on to other cultures as it's just perpetuating a colonial mindset and it really hasn't worked out well on our last three forays with the US into Muslim countries over the past 3 decades. If anything it's made them more fundamental and murderey.
What I'm getting at here is that the sportswashing label is ridiculous on the face of it. These middle eastern theocracies, caliphates and absolute monarchies don't care about what the west thinks of their behaviours. They do care about prestige and the accumulation of wealth, deeds and status, especially when competing with rival states.
As you said people are going to judge us based on how our owners govern and project their power. If you dig slightly under the surface of any of the other owners of other teams you're going to find a sleazy underbelly. US billionaires, Chinese concerns, South East Asian oligarchs, Russians etc etc. Until the Prem adopts a model like the Bundesliga that puts the power into the hands of the fans (lol good luck), it's going to continue to be dominated by unscrupulous types who are inflating their own egos with spare change from their unbelievable fortunes.
When it comes down to it people don't like change. They like the established order of top 6 teams and sometimes an outsider like Leicester busting through. When someone like us comes through to upset the apple cart and oust some of the top 6, they will use what they can to delegitimise us. This happens to be easy with a very obviously nefarious power as the owner. However, glass houses and all that.
Sorry I've been on the vodka again tonight and I've written another essay.