(Years go by...) This is an issue on our site as well, trying to have a survey form embedded in WordPress, with all content https. With some effort, we can find an link to the survey ('questions') that stays https... but then after submitted, the response URL snaps back to http. It seems that best practices would be to maintain the sequence in the same protocol as the request. If a process is initiated with https, it should stay https. (Note in our case, it's not about login -- surveys proceed without a login sequence.)
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