We used Django for this for almost 3 years and had zero problems. Of course, you want to start with a form on an HTTPS page, not just submit HTTPS - it makes people feel safer.
Django does not play the cookie in URL game like some PHP platforms, so if the user does not accept cookies, he will not work.
Do not forget that if you have all this confidential data, you must process it correctly. We only store the last 4 digits in the online database and for verification purposes only. Everything else is managed through connecting the back door to a separate company that manages the subscription for us.
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