What test strategy should be used to test a chrome extension which relies on the DOM structure on various websites?

I have a chrome extension which supports 10 different websites (and the list is growing). These websites are translation editors where you have to log in and I don't have special test account on all of them. The chrome extension relies on the DOM structure or class names and ids of elements in the DOM to obtain data from the websites and send this data to an API. Also the extension provides the user an UI which is a draggable iframe which is being injected into these supported environments.

My question is, what test strategy would you recommend since I am living on a moving ground (foreign websites can change all the time, DOM can change and things will break)