Just to defend myself, let me, mention that the present day calendar has no basis in the Gemara so we have to go by the actual molad, the time when the moon and sun are at the same longitude. Second day of Yom Tov is more complicated. My feeling about it is that the the reason for it is a debate in the gemara. One holds it is  a law derabanan. Rav Asi holds it is a custom [and that is the law]. But it is not a custom dreamt out of thin air. It has a reason. That is perhaps we might forget the actual time and have to go back to witnesses. So I say, fine, let's go back to witnesses. Once the supreme court in Jerusalem determines the date let them send witnesses by airplane. That is the original custom was not based on there not being a court. Rather it was based on not knowing the right time, and thus having to depend on the court.
Now if it would be a custom established by the Supreme Court, then it would have to be nullified by  a supreme court that is accepted by more חכמי ישראל. But the Supreme Court in Jerusalem did not establish it. It was a custom started in Babylon by the local people  because of the worry of forgetting how to calculate the molad and having to go back to going by the Supreme Court which would have to send witnesses. That is why even outside of Israel any place where witnesses can reach in time never has two days of Yom Tov. For example in Mitzraim. Therefore this law has nothing to do with being outside of Israel. It always depends on where witnesses can reach.

The point here is that the reason the religious world ignores these simple facts is not because they are hard to understand. Rather they simply do not care what the Torah says. Their religiosity is all smoke and mirrors. It is the same reason the Supreme Court thinks it can regulate what you grow in your backyard under the interstate commerce clause. It is not that they are so dense as not to understand the Constitution. It is rather that they do not care what it says.