Bernie Sanders has endorsed Clinton and is urging his supporters to go out and vote for her on election day. Bernie failed to get the nomination, and is mature enough and smart enough to know that he needs to get his supporters behind Clinton to avoid a Trump victory. Sanders and Clinton are both Democrats, and both stand for mostly the same things.
Who someone votes for is entirely up to them. For Bernie supporters, the decision should come down to why they supported Senator Sanders in the first place. If it was under the belief that he was the best Democratic option, then they should likely vote for Hillary as she is the Democrat. If it was because they are extremely progressive, they may want to write him in or vote 3rd party.
While Hillary is not their candidate of choice, those that supported Bernie Sanders should cast their vote for Hillary in this election. Her views more closely represent theirs in comparison with Donald Trump's. Perhaps there will be a place for Bernie Sanders in Hillary's cabinet if she is elected President.
If a candidate does not support your ideas then why would you vote for them? Hillary and Bernie differed on so many topics and just because they have the same letter next to their name does not mean that all of his supporters should support her. I also thought that when he endorsed her at the DNC it was one of the weakest things I have ever seen. He should have stood up for himself and said she cheated and she is a liar you guys should support whoever you want.
No, Sanders supporters should not vote for Hillary in the general election, because she was not fairly given the nomination. The democrats should have been fair. It was only because of superdelegates that Hillary won the nomination in the first place. If Sanders supporters fall in line, they're only going to allow the democrats to get away with stuffing the ballot box.