How would you feel about a test for "teal or blue" or "teal or green?" You still need to make binary choices, just along different boundaries. Would it make any difference?
How would you feel if the site showed you red and asked if it was blue or green?
if the question was "is this more blue or more green" it would be somewhat more agreeable. but there really just have to be a "can't decide" option as well.