I'm not saying it never happens to white girls - but that tends not to be where a lot of it (I'd say probably the majority) gets directed, and that matters. I'd also hazard a guess that a lot of the men you're referring to are themselves white - and yes, that's racist, but the racism is still focused outward in those cases, if that makes sense. As to white girls in Asia... well, yeah. That's straight-up role-reversal. Exoticising the other happens all over the place; that doesn't make it okay when we do it, and it doesn't mean we shouldn't be mindful of the context when we're interacting with traditionally-oppressed people.
I would say that, yes, finding another culture sexy is probably racism. Why? Because it's indicative of some pretty extreme ignorance. It's possible to find certain elements of a culture sexy, sure - but if you assign that label to the culture as a whole, you're treating it as more monolithic than it deserves and glossing over a lot.
Costumes in particular can be problematic for reasons that are hard to explain, but... well, the short version is that they're very often used to showcase incredibly shallow stereotypical crap and pretend to be of a culture, without ever having to deal with any of the downsides. (Ask some Native people who take their cultural heritage seriously about Halloween sometime.) The geisha costume in particular is likely to raise eyebrows because it's not just doing that, it's pandering to a specific stereotype which has been hugely problematic and the basis for a lot of racism in the past.
It's not impossible to appreciate other cultures respectfully. But... it's important to err on the side of caution. If you have to ask if something is racist, I'd say that's probably a good indicator on its own that the action in question is at the least problematic - and I would absolutely try to seek out the opinion of someone from the culture in question, someone who can't just take off the costume when it gets uncomfortable. (Important note, though: Be cautions and respectful in your approach, and be prepared to take "I don't want to talk about this." as an answer - being expected to speak for your entire culture is a problem, too.)