Wallace absolutely fits the Brexit voting demo, he's the right age, northern from one of the forgotten industrial towns that feel increasingly disenfranchised by big politics and used Brexit as their protest vote. He tends to only read the same paper and so his views don't ever face any sort of challenge leading to them becoming deeply embedded. He's impulsive and frequently shown to be a poor judge of character so would easily have been taken in by any targeted Facebook memes designed to stir up anti-EU sentiment.
Gromit is younger and a university graduate, he's shown to possess far more empathy and critical assessment skills than Wallace and so we can surmise that he would be well clued in on the social and economic impact of leaving the union. He's also probably quite well read regarding animal welfare rules of which the EU is held among the highest worlds standards in. It's possible that he agrees with Jeremy Corbyn on the issue of the EU's central banking system and its position of maintaining market status quo with small and incremental growth which of course threatens any great socialist objectives through aversion to change but all things considered it is likely he would have voted remain and urged his MEP to try and make changes from a position of solidarity rather than isolation.