For many nonprofits, a common strategy has been to ask supporters to lobby only those politicians who might agree with you. If you're focused on issues like the environment, social justice, education access, reproductive rights, etc., that means reaching out to folks where the political map is blue or purple. You then have your supporters apply pressure to advance policy that their elected official might be open to supporting. For your folks in districts with elected officials opposed to your specific issue, the best ask of those supporters has been to write you a check...or organize for the next election cycle. Why ask them to waste their breath trying to convince a member of Congress who's never going to vote for your bill?
But now that our entire political system seems to be on fire, we should change that approach. You should be mobilizing the heck out of your red district supporters, asking them to deliver the message that the broader path we're on is not okay.

When a Republican member of Congress like Lisa Murkowski says, “We are all afraid” of retaliation from the Trump administration, that’s an opening. An opening to remind our elected officials that there’s political cover for standing up to despotism. That we should all be against the undermining of core democratic institutions. That Congress shouldn't be giving away its power to the executive branch, and Republicans and Democrats alike should be fighting against conflicts of interest and the kleptocratic habits of our current administration.
There are Republican politicians out there who are worried about the Epstein files. They're worried about the yawning national deficit and program cuts that will hurt their voters. They're worried about the ongoing decimation of agencies that most Americans consider critical. There's an opportunity right now to break the thrall they're in, but only if you're a constituent. So find your supporters who are constituents in red jurisdictions, and do all you can to connect them with their members of Congress.