My response is something I tried to argue several years ago. The right psychological approach is to ask people to call upon their personal experience with climate in past years to help them overcome a prejudice that we've not affected the climate. What might be hardest for science realists is to accept that it's not a bad thing to call upon personal experience, because we're not asking people to be scientists but only to contribute to the overall decision-making.
For example, let's talk about the fascinating subject of my teeth. Here in America we still have debates about whether to fluoridate the water to prevent cavities. I've lived in a bunch of different places in the country, and two of them - Alaska and Portland Oregon - didn't fluoridate. You can guess which two times of my life when I've had the most problems with cavities.
Now it's hardly scientific to draw conclusions based on my experience, but if I made my own decision on whether to vote for fluoridation based on my experience, and aggregated my vote with others doing the same thing, then you'll get something approaching a reasonable scientific judgment as well as the right policy.*
The same thing is true for climate. Anyone over the age of 30 can remember a modestly different climate in the past, and everyone knows older people who can tell them about earlier periods when it was even more different. People can feel it in their bones that the climate's gone screwy. That's what we need to latch on to.
Yes, huge amounts of noise in this type of data, and yes, urban heat island and urban migration can confound perceptions, but people can adjust for urban heat if they want in their personal experience, and millions of human data points are being aggregated to filter the noise. My point is that it's not invalid to call upon these experiences.
The other issue is the claim by denialists that it's just coincidental warming. The way to handle that is to latch on to the fact that people like patterns and don't like coincidences. Point out that the people who are arguing that it's just a coincidence are the same ones who still dispute the scientific record that shows what we feel to be true, that the climate has changed, that it's gotten warmer, that weather patterns are different. It is not a coincidence that the people denying the warming are making that argument - they don't like the implications of it. Again, personal experience of how much the world has changed could help people consider whether our modification of the planet could be responsible for the modification of climate.
So this may not be the scientific ideal approach, but it's not invalid, and it could be a way to make progress.
*I'm ignoring the alleged low-frequency dangers of fluoridation, which isn't really relevant to the analogy I'm making of people drawing on personal experiences to understand whether fluoridation prevents cavities/that climate change is real.