I don't have any experience with purple okra, but if that's all I had, I'd try it. Who knows, it might be beautiful! I would consider using white vinegar instead of apple cider, to let the lovely color shine through. And if you have access to hot peppers before they turn red...when they are sort of a yellow-green color...that would really pop with the purple. If you do it, please report back.
I did find some info at this link by searching Google images....

Here is a link that might be useful: Pickled purple okra from a blog

Hi, I just pickled 6 pints of a combination of Clemson spineless green okra and Burgundy Okra. The burgundy okra colored the white vinegar a beautiful pink color. The burgundy color of the okra is now muted, just like the green of the other okra turns a little. I used a bright red pepper in mine and I think the jars are beautiful. Next time I will try to pickle the colors separately just for something different.

Lyle, I pickle purple okra every year. I always grow burgundy okra. It doesn't stay purple, but as gardengirll said, it turns the white vinegar a pretty pink.

Judi

Thanks for the responses, I will go ahead and give them a try. I have a recipe, but if anyone thinks that they have a "killer" recipe, feel free to pass it along. I like the hot pepper idea to spice them up a bit.

Lyle