Sorry for comming back to this topic. I just wanted to write that I had the same problems as the guys here.
The reason was that my Raspbian (on RPi 3) couldn't sync date/time properly... (That is very strange, as previous installation worked perfectly. Then I had to reinstall Raspbian and now I've been having problems with time sync).
Installing ntpdate solved the issue with https websites. So, if anyone in the future will have similar problems, setting your time/date properly is first what you should do