According to who? Who told you that is their agenda? So what is the motivation for a Western country trying to get a World Cup, for instance? Is the immediate assumption that it could only possibly be to I dunno, deflect, away from any sort of negative perception of their country? Or are they immediately separated from each other because 'it's not the same thing' (obviously).
Qatar, like ANY other country, are using sports to advance their country in the same way that ANY other country would want to use it to advance theirs. The immediate surmising that any progressiveness from the ME is 'sportswashing' is ridiculous and xenophobic in and of itself to me. It's saying that the ME should be identified solely by their rightful position in the world as evil barbarians and shouldn't try and 'buy their way into the light'. My point is, your definition of them is likely not the same as their own of themselves. They are simply a sovereign state, with leaders who have the responsibility to do what they feel is best for their country. If your conclusion that Britain bidding for the Olympics in 2012 was not an effort to 'wash' away any stigma held about them from Iraqi invasion, then I see zero reason for Qatar hosting a World Cup or daring to try and do something good for their country being dismissed as such. I'm sure you took Iraqi invasion and Olympics 2012 to be totally disconnected.
Qatar would not be doing anything to 'repair a tarnished reputation', they would be making moves to grow their country just as anyone else would. What you choose to think of them is up to you. In the grand scheme of things, why would they give a shit about whether you agree with their policies or not anyway? The only way it would affect them is that you may choose to not go there on holiday and contribute to tourism. Which is a right that you still reserve whether or not they own United.
This sportswashing thing just says 'we have labelled you as the evil bad guys, stop trying to confuse things by doing anything good. We've already decided not to like you, please make it easy for us by only killing people'. Perhaps if they make a medicinal breakthrough you would be like 'there you go again trying to not accept who you are'. Even taking your statement at its most literal, clearly you have an issue with a nation wanting to repair its reputation.
They are telling you that there is more to their country to homophobia and anything else you don't like, but you have a problem with them being associated with anything other than that, clearly. Who are you to decide that is all they're good for? Do you think Arabs agree with a country where men wear makeup and tight dresses, change genders, get into drunken and drug fuelled debauchery? Probably not, but yet they still come here for the bits they like. They still engage in the sports, still do business. That is because clearly that is not all they associate with Western states. There is good and bad, and people need to accept that there is good and bad in Qatar and ME states. If you choose to not engage with them at all on the basis of the bits that you don't like, it is of course your own right - but they still have a country to run and develop, and there's no reason why they shouldn't look to do so without everything being done from the context of the things you don't agree with.
I've said before in this thread - Qatar just hosted a whole World Cup. They did NOTHING to conceal the fact that they despise homosexuality and drunkards, for example. In front of the cameras, they banned pro-LGBT displays and banned alcohol. They are not as invested in how you view their views on these things as you think. They simply said this is how we do things, now we'll get on with the business of hosting a great World Cup. Which they did. You could choose not to go, that's fine. But they didn't pretend that they were not anti-LGBT so that you could come and like them. But because they are not pro-LGBT also didn't mean that they should not get on with doing what is right for their country and putting on a great show.
The dismissal or simplification of ME sports projects as 'sportswashing' is just a western superiority position for me. Hosting the F1 would appeal to them for the exact same reasons it would appeal to Britain.