As someone who has extensive experience in NOT being politically steamrolled:

#1) Trevor Noah and John Oliver have never changed a mind, don't emulate them. There is no audience. There are no punchlines. If you feel the urge to "dunk", stop.

#2) Avoid the association to politics and identity as long as possible. This is where all the conflict is. People have made politics their identity (this is NOT exclusive to the right). As soon as a conversation is perceived to be an attack against their identity, the productive avenues for discussion are over.

#3) Talk about things outside of the context of politics. They probably have someone in their extended sphere struggling with pain medication addiction. Or mental health.

#4) Allow them to in the course of the conversation rebuild their identity around the non political compassion for the people they know who are struggling. Because they probably have that

#5) After a discussion where you're agreeing with eachother the whole time about how crushing something has been for people that they've seen, you'll be at a point where they just assume you have the same politics. Why wouldn't you? You've had a deep conversation and you agree about the existence of some big problems... That's when you can let it slip. Not "dunk", but slip, about how this is why you're jazzed about some specific POLICY that could help. It just happens to be a liberal or NDP one.

Honestly it's not hard. If it's hard you've been watching too much media designed to sell left to left. You don't sell left to right the way you sell left to left. Step away from politics and re-learn how to have a normal conversation first.