In fact, after long comments and explanations, this leads to the fact that for EF there will be a default membership of MemberhipProvider, and - guess what, guess what - it is called EFMembershipProvider. Here's a link. Now this is really great, because third-party implementations of the MembershipProvider will no longer be needed (or the corresponding manual implementation - it was a kind of BIG and complete excess for small projects).
UPDATE Currently, this provider seems to be unavailable. I do not know whether it will develop and be included in the future.
Since we are encouraged to use SimpleMembershipProvider and migrations when using EF Code First, this is what I am doing now. You can also implement ExtendedMembershipProvider, which requires a bit more effort.
For me, the best solution at the moment is to inherit from SimpleMembershipProvider and change only those things that I need (I use most of the code from my previous implementation of MembershipProvider), for example, registering by email or username.
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