Okay
did some research on this.
Updated: I think I figured this out. The argument is going to be that Cohen gave Trump a personal loan as his lawyer, in his professional capacity. It's then incumbent upon the Prosecutor to prove- beyond a reasonable doubt- that this was done purely to help Trump with his campaign. As a gift, that's a REALLY easy case to make. No one just "gives" $130k to someone a few days before a campaign to make something go away. And if it's a gift- it's almost impossible to make the case that the communications revolving around the payment are covered by attorney-client privilege.
Loans are still illegal campaign contributions if they're given for the campaign, but if this is a personal loan given in the capacity as the candidate's lawyer then it's potentially a different story. Personal loans to a candidate- even from a political supporter- aren't actually illegal. It's a gaping loophole. And if they argue it was done in the capacity as his lawyer, then there's an argument to be made that all relevant communcation about it between the two (the communication you would almost certainly need to prove this was a campaign contribution) are then covered by attorney-client privilege and therefore are off-limits to the Prosecutors and the investigators.
It's a potentially risky strategy as the crime-fraud exemption is arguably in play, and it opens Trump up to campaign violation charges (and there's no protection for crimes committed before you enter Office) But they may be banking on the fact that the Prosecutors won't have enough evidence- absent the privileged communications- to convince the Judge of that fact.