Bold of you to assume that little twat has any political power whatsoever. He's being led around by the balls by the Ferrymen.
He still has some info, and the Ferrymen still get info from him about you (though I'm sure they have plenty of their own sources). If playing along gets you even just the smallest iota of info that helps or leads the Ferrymen to believe you're in their pocket even just a little bit more than you actually are, it's worth it for now because it costs literally nothing but perhaps a tiny bit of pride and patience. This is particularly true if Dante later on comes to regret teaming up with the Ferryman and
himself becomes turncoat and willing to tell you everything he knows because you're still 'friendly'.
And if you have no interest in that, it's still a dumb move to burn that bridge now for no reason or benefit other than feeling good. Burn it later when you actually can get something of value out of it at the same time or when pretending to still be on his team would carry a cost. And as long as they think you're an 'asset', they aren't likely to actively move against you. If they now think you're an enemy asset, you've just added additional risk to yourself you didn't need to.
Like it or not, MC is now in a position of political power and really should be thinking about and playing the long game if he wants a good outcome for himself and those he actually cares about. It's an unforced error, strategically, to reject Dante now unless you for some reason think telling him you can't promise to be on his side will cause him to see the error of his ways (strong doubt on that one).
Edit: Now, it
is possible someone oversaw your exchange with him and maybe recorded it as evidence to use against you with Faustina et al, but we haven't been shown that yet. And honestly I don't think it'd be too hard to explain away.
I will however be pissed if taking his hand there locks me into taking his side later without giving me another choice when it actually matters.