Sorry, I don't get it...
...a spiritual exercise...
The researchers' use of "religious" and "spiritual" is (dare I say it?) very American. As far as I can see, "religious" is conventionally-moral socially-conservative follow-the-rules-and-get-to-heaven Christianity, while "spiritual" is just about anything else but especially new-agey feel-good pop mysticism.
That's how they can say, "conservatism and religiousness both emphasize the importance of tradition, while liberalism and spirituality both emphasize the importance of equality and social harmony." It's also why they can run an "experiment" as simple-minded as the one described ...
In the third study, the researchers recruited 317 participants from the U.S. and asked half to complete a spiritual exercise consisting of a guided meditation video. Those who watched the video were asked to close their eyes and breathe deeply, imagining themselves in a natural setting and feeling connected to the environment. They were then asked about their political orientation and to rate how spiritual they felt.
... and claim the results mean something.
In case you hadn't noticed
I am not very impressed by what they have done. Nevertheless, I agree with their conclusions.
I reached the same conclusions myself, years ago. Even earlier, my father expressed them, indirectly, in his comment on politics: "If you vote conservative before you're forty, you haven't got a heart. If you vote liberal after you're forty, you haven't got a head." (At the age of 15 or so I decided that I would rather have a heart than a head, regardless of my age, and you may be glad to know that my voting has indeed moved further left as I get older ... but that's drifting off topic.)