How should I go about wearing this scarf?

Scroll down and you get a picture of a little girl wearing one. https://en.m.wikipedia.org/wiki/Keffiyeh#/media/File%3AA_Palestinian_girl_with_a_Palestinian_scarf.jpg

I don’t think it’s an issue to wear it. It doesn’t appear to have any religious connotations to it, it is just used to keep them cool.
The Wikipedia article you linked said it became a fashion accessory in the United States in the 80s. So the only comments you might get would probably be about the fact it’s out of style/outdated.

Lots of choices – see link

If there’s any chance that it will be interpreted as a political statement, I’d say be cautious. It’s one thing to deliberately make a political statement of your choice, and it’s another to innocently and unwittingly wear, say, a T-shirt with a black fist on it or a rainbow flag. Those are symbols that mean a lot to some people and might draw reactions you’re not expecting if you don’t understand them.

I’m not saying don’t do it—I’m just saying you’re wise to try to find out beforehand if it carries more meaning than you intend to convey. Including among those who are ignorant of its actual use and instead react to stereotypes and associations.