That is a very myopic way of looking at it. Right-wing neoliberal parties were globalists and pro-EU for business reasons. Left-wing social-liberals were pro-EU for social and ideological reasons but were much more ambivalent about globalisation. Hard-right nationalists hate the EU but don’t see much of a problem with globalisation except when people are involved (exploiting them abroad, however, is fine as long as there is a buck to be made). If you’re a bit careful you’ll find opinions all over the place on both globalisation and the EU across the whole spectrum.

Globalisation is more something that affect individual member states than a EU issue.