Or you can just decline to answer. The form is there to keep general tabs on overall racial statistics. It doesn't affect you in particular, and it's always optional.
Nobody else is likely to ask your race. It just doesn't come up.
HOWEVER -- others may assign you to a race. It doesn't matter how you identify. If they think you look black, or Hispanic, or Asian, they'll treat you that way. It won't do you any good to say, "No no, I'm raceless". It wouldn't even do you any good to say, "No, I'm not Arab, I'm from Bangladesh".
That's the reason some forms inquire about race. They want to see if there are any patterns of racism, so that they can look for ways to manage it. They ask you for your self-identification, which is usually close enough to what other people assign to you, at least for statistical purposes.
If you write in "raceless" you're just opting out of that record keeping. Or at least, you're going into that "other" category, and they'll keep an eye out on trends in that dimension.
But you won't find people ostracizing you for how you identify. They might ostracize you for what you look like, rather than how you see yourself.
If you say "raceless", it'll probably either get a "uh, ok then" kind of response from people who don't really care (bureaucrats who just need to fill out a form they have no control over), or you might invite a discussion like "what's that? what do you mean? where were you born?" Do you want to have that convo? It's probably not going to go anywhere useful outside of controlled contexts like academia or a group of friends.
Race is a pretty taboo topic here in polite contexts between strangers.
On the other hand, if you really want people's unfiltered thoughts on your race or lack thereof... plenty of places online where you can spend a lifetime arguing over it. Not necessarily a good use of time, mind you, but people will definitely have opinions...
People don't discuss or act on race very often here, at least not overtly. You may be reading too much reddit or Twitter.
Are you trying to identify as raceless to make political statement? Or is it more a case of "mom was half Native American and half Chinese; dad was half Afro-American and half Danish"?