Here's a tutorial: https://www.hgtv.com/design/make-and-celebrate/handmade/how-to-customize-a-plain-shower-curtain-with-paint
Yes if you get a cloth shower curtain you can paint it with chalk paint. I painted this drop cloth rug I made with chalk paint. And I have washed it and it washed beautifully. I didn’t dry it though. https://lifeonsummerhill.com/diy-rug-out-of-a-drop-cloth-and-chalk-paint/
You can with Amy Howard One Step Paint.
You can paint a canvas drop cloth and use it as a shower curtain.