I'm a true blue conservative (well, wish the actual Tories would be as well, but that's another story) and I work in finance and interview graduates.
I wouldn't assume everyone in finance at junior levels is keen on the Tories - you do get well-meaning lib dem types, and people in HR also may be more social justice-y with stereotypes.
Also keep in mind that even actual card-carrying Tory party members often find Young Tories really obnoxious - remind your son to not turn up in a tweed suit... Although if he's into finance he might be better able to seem normal than the ones who become spads.
With that said I think it would be fine to mention the activities, say "a university society", if pressed say "a political society - I'd prefer to focus on my activities in the role rather than the politics, I hope you understand..." and if really pressed then say "the Conservative party" without sounding apologetic, just neutral/straightforward.
It might be worth preparing a couple lines about why he supports them, which relate to finance and the importance of the City of London to the British economy blah blah rather than brexit or immigration or trans issues or something. Don't volunteer them but good to have on hand if for some reason interrogated, so he can transition the convo back to why he is passionate about finance etc.
Also this isn't PC but I mean, read the room and signals from the person, there's a difference between the HR interview and the partner chat. I still wouldn't go into full campaign mode and would try to focus on the finance industry etc, but it would be weird to not name the party in the partner interview and probably is safe to do so. Sorry for long response but good luck to your son