71% of Labour's voters voted remain. Not pushing hard for a Vote on the Brexit deal would split the party. The economic harm will hit working classes most; Labour, as guardians of the workers, would be blamed.
The "benefits of the Single Market & Customs Union" mean following EU rules but no longer setting them. i.e. out of the EU with less control. Labour gets blamed.
We're protecting Labour from that!
Say Brexit happens. There's a transition for 2-4 years where the economic hit is minimal. Just in time for Jeremy to be left holding the bag if he wins the next general election. The economic damage will be blamed on him and the very concept of socialism.
It's reputation will be destroyed if it chooses getting power or narrow ideology over the wishes of its members/voters and the good of the UK.