It stems, I suspect, from disagreement over what "neoliberal" means: a mixed state being at its heart, most all social democrats support a strong, competitive market economy; neoliberals wanna cut the state back to the bone, along with regulation that saves capitalism from itself.
As for the EU treaties being neoliberal: yes, they're undoubtedly pro-market, particularly the four freedoms; but they also impose significant restrictions on the freedom of companies to do what they like (short of a handful of narrowly-drawn civil wrongs).
It's true that changing them's hard, but that's directly tied to the EU being an alliance of nation states, and not a federal republic. If there's popular will across Europe, with a social democratic bloc in the European Parliament, and a majority of European governments being social democratic, there'll be a powerful mandate for change. People can "campaign for progressive groups" until the heat death of the universe and it will be a complete waste of time in so far as altering the neoliberal nature of the EU is concerned.
What's the alternative? The EEA? Bilateral trade treaties between European states, without any of the social directives? They'd allow European countries to cut wages and protections as they raced each other to the bottom. That'd undoubtedly make the buccaneer free market crowd happy, but it wouldn't do much for workers' rights.