Probably to get him on their side
From James Potter and the Hall of Elders' Crossing:
It shocked and worried him for a moment. He was irrationally afraid
that somehow his thoughts had gotten out and betrayed him, that it was
the noise of the Gryffindor table standing, booing him. But it wasn’t
the sound of booing. It was the sound of applause, polite and
sustained, in response to the calling of his name. James turned to
the Gryffindor table, a smile of gratitude and happiness already
lighting his face. But they weren’t the ones applauding. They sat
there rather blankly. Most of their heads were turned toward the
source of the sound. James turned, following their eyes. It was the
Slytherin table.
Tabitha, the girl who initiated the applause, later approaches James and seems to want to be friendly and put old enmities aside:
“No, no!” the pretty Slytherin girl said, raising her hand toward him,
palm out, stopping him in his tracks almost as if she’d used magic.
“Don’t stand. I’m happy to see you feel comfortable enough to sit at
the Slytherin table with us. These are quite different times than
those of your father. But I assume too much. Mr. Deedle, would you be
so kind as to introduce me to your friend?”
And indeed, Tabitha was behind the Progressive Element:
James hadn’t, actually. “Doesn’t really matter. It was the Slytherins
that got the whole thing started, with the Progressive Element slogans
and badges and stuff. You said so yourself, Ralph. Tabitha Corsica was
handing the badges out to all the Slytherins. She’s behind the whole
thing.”
It seems likely that the purpose of the applause, which was initiated by Tabitha, as well as Tabitha's own overtures toward James, were meant to make him sympathetic to her cause.
If the son of Harry Potter, the hero of the war against Voldemort, could be seen to endorse PE ideals, it would be quite the coup for their group. Even if he was merely seen associating with them, it could be a potent propaganda tool, for recruitment and other purposes.