I'm not sure it counts as an example
I don't recall any "unity" being displayed during Slug Club meetings. Certainly, there were students from various houses. Harry and Hermione were there, as Gryffindors. There were also Slytherins, such as Blaise Zabini.
But were they cooperating? No.
Harry and Neville purposely ignored Zabini:
Zabini did not make any sign of recognition or greeting, nor did Harry
or Neville: Gryffindor and Slytherin students loathed each other on
principle.
—Harry Potter and the Half-Blood Prince
And later, Harry and Zabini demonstrated their feelings more openly:
As he pushed past Harry into the darkening corridor, Zabini shot him a
filthy look that Harry returned with interest. He, Ginny, and Neville
followed Zabini back along the train.
—Harry Potter and the Half-Blood Prince
There was not "inter-house unity" here. Quite the contrary: the animosity between Gryffindor and Slytherin was on full display. These students were more or less forced to be together by Slughorn's insistence. They did not enjoy it.
There is no indication, to my knowledge, that Harry, Ginny, or Hermione changed their opinion of Blaise while in the Slug Club, or that their interactions with him influenced their opinion of Slytherin (or vice versa).
Besides, the Slug Club was rather small. There may have been more in the movies, but it would seem that in the books the Slug Club was mostly those students whom Slughorn gathered in his compartment on the Hogwarts Express.
But even if it did, there is a much better example
The best example of inter-house unity is the Battle of Hogwarts.
- Members of the three non-Slytherin houses fought from the beginning.
Despite McGonagall's attempt to get rid of all the Slytherins, they went for help, and Slughorn at least returned to fight against Voldemort:
And now there were more, even more people storming up the front steps,
and Harry saw Charlie Weasley overtaking Horace Slughorn, who was
still wearing his emerald pajamas. They seemed to have returned at the
head of what looked like the families and friends of every Hogwarts
student who had remained to fight, along with the shopkeepers and
homeowners of Hogsmeade. The centaurs Bane, Ronan, and Magorian burst
into the hall with a great clatter of hooves, as behind Harry the door
that led to the kitchens was blasted off its hinges.
—Harry Potter and the Deathly Hallows
Furthermore, the Malfoy family (all Slytherins) betrayed Voldemort in this battle, as did Severus Snape. Narcissa Malfoy even expressly colluded with Harry, a Gryffindor.