4 jobs in 3 years would hurt my chances on a Top MBA?

I think it depends on the transition. If it's a logical one that supports your goals and advances you up in the industry (to a regarded fund, not for a promotion or pay) than I think you can articulate it.

The risk is that you're viewed as a promotion/pay hopper. If you can tell a story around moving towards your goal then that can be helpful.

However, I think your hunch that generally, not having 1.5-2 years in a role is harmful is probably accurate.

B-school will be evaluating your resume much like an eventual REPE fund would. If you can read your resume from that perspective and honestly think the next move would logically move you more towards REPE, than the negative effect might be partially or totally offset. I'd be very, very picky about what that move might be however. Remember that regardless of whether or not you make that next move, you will be generally be competing for the same post MBA role and pay. In REPE, your pay might be negotiable so a huge bump now might be helpful, but make sure it doesn't come at the expense of the REPE shop viewing you as a liability down the road. My outside view (I am consulting track at Booth) is that REPE funds hire interns for the short term but make full time hires for the long term and the expectation will be that you're there to stick around. All else being equal, showing some of that commitment now would be a check in your favor.