Recent polling has shown that of those who voted Brexit, very few have changed their mind, indeed it looks like their opinion is hardening. It is those who didn't vote who have pushed remain into the lead in opinion polls.
The potential negative impact of Brexit is widely known, the government's woes the same - it had made little difference to people's opinions. The unions are not all ardent remainers so there is no consensus there either.
Politically, Brexit is a shit storm and the only thing that would happen to Labour if they adopted one position strongly over another is they would be riven by the sort of problems the Tories have or become politically irrelevant like the Lib Dems.
There is no knock out blow to be had, the Tories will either self destruct on the back of their own failings or they will escape with a last round knock out of a Brexit deal, there is no middle ground. Labour's best hope of doing something about Brexit is by being in power, not by being in opposition.