Not that simple. There are many factions in this game, and they cross party lines.
It’s not just about in/out. It’s about what “out” should look like.
May has presented the negotiations as “getting the best deal possible”, but there is no consensus on what that should look like. She wants the status quo minus free movement. Most Tories are pro-free movement because they’re pro-business and business doesn’t want labour shortages pushing up wages.
Corbyn is at war with his own parliamentary party and membership and voters. He thinks we can restore wage bargaining power by restricting immigration, and shore up British industries with trade barriers and State support (at least I think that’s what he wants, but maybe he just wants to nationalize everything because he’s a lunatic socialist). A decent chunk of Labour supporters see restrictions on free movement as being driven by racism, and are therefore ideologically opposed, the “I am a citizen of the world” types. Another chunk vote Labour because they’re poor, and support Corbyn’s effort to restore wage bargaining power through labour market controls.
And the DUP don’t give a shit about any of that. They are the real identity politicians.
So I really don’t see how you can view this as a “both sides” thing.