That picture is from 2008, 16 years ago. Hardly the same social sensitivy toward race issues in 2008 than in 2024, not only in Spain but everywhere else, including the US. I remember the American model Gigi Hadid some years ago posted a picture simmilar to Badosa's one ("mocking" Asian eyes) and she receieved a lot of criticism for it. Saying the US are racist due to Hadid's behavior is an overgeneralization based on the mistake of one individual (if you really believe the US as a whole are a racist country, you would need more than this anecdotical evidence to make such claim). Analogously, Badosa mocking Asian eyes in this era of bigger sensitiviness and awareness that is 2024, just proves she's dumb, but it doesn't mean Spain as a whole is a racist country. That is overgeneralizating from the dumb behavior of one single person, and disrespecting the other 46+ million Spaniards that have never mocked Asian eyes in any picture or form.
P. S.: for me, the biggest argument you could make that Spain has a "racism" problem is if you consider the social perception toward (especially illegal, and specifically from Moroco and Sub-Saharan Africa) immigration. Many people in Spain oppose to migration from the Moroccan Islamic community, which is entering here massively and in many cases it is done illegaly. Also happens a lot with the sub-Saharan African community. Many have the perception that those inmigrants are unfairly receiving social help payments from the local government, instead of the locals receiving such economic distribution. There's some sort of overall social rejection of the Islamic people and its culture and religion, as well as a rejection of the sub-Saharan African illegal immigration (which is being massive and has no control in some regions such as the Canaries, giving problems in terms of resources and social structures to receive them being saturated). But still, the most voted political party, the one in power, is PSOE, from the left wing and 100% pro-immigration, an openly "woke" party. So it's far from clear that most people here have such mindset, though it is very common.