Reptile mites are...well, reptile mites. They can and will feed on any living reptile. There is no such thing as an "iguana mite" or a "leopard gecko mite". I personally have had success with Black Knight "roach killer". This product is currently not in production, and the dealers that do have it are hoarding it. Thankfully, I have no mites, and half a can of BK. Provent-a-mite has been recommended and used with some success. If the creatures in question are not infesting your frog, I doubt they are reptile mites, or even mites in general. Reptile mites NEED to feed on the blood of a reptile, and presumably an amphibian. If they are avoiding contact with your frog, chances are they aren't a serious problem. Still might want to get rid of them though, because the only life you want flourishing in your frog tank is...well, your frog.
Keep in mind, Black Knight (if you can even get ahold of it now) is not to be recommended for use on amphibians (at least by me). Amphibians soak up much more through their skin than reptiles do. So please use discretion, and try other methods with your frog (i.e. making sure your frog is mite free, and THOUROUGHLY cleaning it's cage).
Mites are a serious problem, and NEED TO BE ERADITCATED! Take all necessary actions to rid your collection of mites! If the little creatures (if they are white, they are probably not reptile mites) are mites, they will quickly (mites can travel up to 40 ft. per hour) infest your entire collection!
And Nevin, soaking snakes in vegetable oil is a horrible way of getting rid of mites! Please, find another way.
Hope my suggestions helped, if just a little.