Cubs BABIP's really aren't that abnormal. There's 3 guys in particular I'd call oddly low and that's Zobrist(.241), Rizzo(.252) and Schwarber(.227). Heyward at .284 is a little low but it's not super significant. Bryant is above .300 but possibly low for him given his career rate is .341 and his rate this year is .313. But the thing is you then have guys like Jay who is at .372. So it happens.
As for the "why" on Zobrist, Rizzo and Schwarber 2 of the 3 should be fairly obvious. Schwarber and Rizzo are lefty power bats that almost exclusively see shifts. Schwarber's numbers are likely a bit skewed as well given he wasn't hitting well prior to june. Since july 6th Schwarber's BABIP is .341 and he's hitting .256/.341/.564 over 88 PAs. If you take that back to the start of june it's .279 BABIP and .234/.336/.548. I think you could argue the difference between him today and him in June was some slight luck variance given his power and on base are roughly equivalent but the hits were slightly lower. On Rizzo, even at .252 BABIP he's really not that far off his career numbers(.285). It's low but not enormously low.
Zobrist is more flukey. He's a career .289 BABIP guy. I'd have to dig in more to get a full picture of what's going on. His power is also down which is weird because his soft contact rate is down from last year(15.4% last year to 13.8% this year) and his hard contact rate is up from last year(32.5% vs 33.3%). His line drive rate is down and his ground ball rate is up. I'm sure there's something there but i'd want to look more into it than the 3-4 mins i just did.