I just had to go through at least 20 screens of the dumb thing, its looping the same images too. I'm on incognito firefox so I can remain logged in on my other account.
@OneEPatternataTime: Not to say that perhaps Etsy has set the reCaptcha required threshold too low, but it is Google that determines the score which is compared to the threshold. Would not be surprised if incognito mode negatively affects Google decision as to whether or not you are a human.