1. No parliament can bind its successor. Otherwise the 1975 vote would have been good for all time and the Jocks wouldn't have been talking about an IndyRef 2. Which, btw, has been derailed by the general election. People voted to say there was no longer a majority in Jockland for the party wanting independence.
Likewise, the two parties promising a hard Brexit got only 44.2% of the vote (and a minority of seats.) So over 55% voted against a hard Brexit and there is no majority in the HoC for such.
2. And no, a softer Brexit would not be a betrayal of the vote. Only of some people's interpretation. Were people asked if they wanted to stop free movement? No. Or leave the EEA? Or the SM or CU? Or if they had a problem with rejoining EFTA? No, no, no and no.
Basically, if they had wanted those questions asked, they should have done so at the time. They didn't.
And if the voters had wanted to answer those questions themselves, they should have done so this month, when they had a chance to vote for the two parties promising a hard Brexit. They didn't.
They didn't. The referendum didn't ask, ad therefore didn't answer, these questions. The GE did. And a majority of voters and of MPs said the answer to a hard Brexit is no.
If the voters don't like this parliament giving a soft Brexit, they can vote for a hard Brexit party next time. {Just like if the Jocks do want IndyRef 2, they can all go and vote SNP.}
We can join EFTA, which wasn't precluded by the referendum, and then voters can vote for a party promising to leave that or promising a referendum on leaving.
Sorry, but if you believe in GB's parliamentary democracy, then you have to accept that the answer to questions given in a recent GE trump questions not asked in a prior referendum.
Hopefully we can rejoin EFTA, wait for the OAP Brexiters to die and then rejoin the EU.