An argument I have often heard is why are people talking about getting a softer Brexit (by staying in the Customs Union (CU) or Single Market (SM) for example) when what we should be doing is staying in the EU. There is a more extreme version of this which says that attempts to get a soft Brexit are dangerous, because they make the prospect of remaining in the EU less likely. I will call this more extreme position Remain fundamentalism.
I want to argue against Remain fundamentalism by imagining a soft Brexit that involved the UK staying in a comprehensive Customs Union with the EU and staying in the EEA. (For an excellent discussion of what the EEA is and is not, see Ian Dunt here, here and here - in that order.)  That is what the current UK withdrawal bill specifies as amended by the Lords, so let me call this the Lords’ Brexit. Compare this to the only hardish Brexit deal that can be done (assuming, as I think is reasonable, that parliament would never pass No Deal), which is something close to what John Springford and Sam Lowe have called the Jersey option: staying in the CU and the SM for goods but not services, perhaps allowing some UK flexibility on freedom of movement.
We have no idea whether the EU would accept either option, because the UK government has been wasting its time (which given they are supposed to be running the country on our behalf is also our time) trying to choose between fantastical solutions to the Irish border problem that the EU will not accept. But for the sake of argument suppose that May ignores her Brexiters, and perhaps with parliament’s help chooses something like the Jersey option and that the EU agrees to it, or instead that May has to go with the Lords’ Brexit and the EU (and EFTA) agree to it.
The Remain fundamentalist argument is that because the Jersey option does more economic damage to the UK than the Lords option (because the EU has a comparative advantage in exporting services, and immigration from the EU is beneficial to the UK), it is more likely that parliament would grant a referendum on it and that people would reject that deal in favour of staying in the EU. I actually think the opposite is the case, We are much more likely to see parliament grant a referendum if we go for the Lords’ Brexit, and that people would reject the Lords’ Brexit in favour of staying in.
The case for a referendum on the final deal is much more clear cut if the deal is the Lords’ Brexit, because the Lords’ Brexit has virtually no advantages compared to EU membership and a clear disadvantage. In practice being in the EEA would mean accepting rules adopted by the EU with no say on those rules. In short, we gain nothing by having no say on the rules we have to obey. I cannot imagine any politician being able to get people to vote for the little bit of wriggle room and influence being in the EEA gives you compared to the having a real seat at the table.
In contrast, with the Jersey option things are much more complex. There will be perceived advantages of this option compared to staying in, such as greater control over immigration. You can be sure that the more Mrs. May can fudge the agreement such that she can pretend these advantages are there even when they are not, she will.
Now add in a powerful group of Brexiters. They would angry that they did not get the hard Brexit they want, but in the Jersey option they would still see hope in ambiguity. More importantly, with the Jersey option there would be plenty of meat for this group to work on, including immigration of course. But with the Lords’ Brexit it is hard to argue a strong case for why this is preferable to be in the EU, even if you are a Brexiter politician or newspaper.
I would be the first to admit that these arguments are not clear cut. But the Remain fundamentalist position only makes sense if you can be sure that a harder Brexit makes a referendum more likely. To me, at least, it is not obvious that it does. The more you can eliminate the economically damaging but superficially attractive aspects of Brexit, the more chance people have to see that the whole thing is a complete waste of time.
 There are a lot of differences between being part of the EEA and what is called BINO: the UK being in the Single Market and Customs Union and everything else to do with the EU except being absent from its political structures. I am assuming that there would be no problem being in the EEA and a CU, that agreements with the EU would also be made on agriculture and fisheries that would at least allow a soft Irish border, that the EU and EFTA would allow all this and so on.