Etymology of English words is somewhat interesting occasionally, but when a key word in a discussion is used in highly differing ways it becomes more interesting, yes.
faith (n.)
mid-13c., faith, feith, fei, fai "faithfulness to a trust or promise; loyalty to a person; honesty, truthfulness," ....
From early 14c. as "assent of the mind to the truth of a statement for which there is incomplete evidence," ..."
faith | Origin and meaning of faith by Online Etymology Dictionary
So, there, starting early 14th century is the meaning which later would make it a good translation for the clear intended meaning in the gospels:
5 The apostles said to the Lord, “Increase our faith!”
6 He replied, “If you have faith as small as a mustard seed, you can say to this mulberry tree, ‘Be uprooted and planted in the sea,’ and it will obey you."
Of course, very obviously the meaning here isn't to merely be loyal to a person or a group or a tradition, but something else, as the context of the gospels overall makes quite certain. (we could also surmise then that only some relative few have the 'faith' meant here in this indication of what real 'faith' is.)
But for the OP using 'faith' in merely the sense of group identity and belonging...then the OP question and answer become pretty straightforward and obvious: 'yes' to whether a group identity faithfulness is at play in some knee jerk reaction to the reality of human caused global warming -- to deny it -- just a political identity (part of the tragedy of the republican party over the last few decades), of no great long run significance, as already the globe has decided to change to other forms of energy and is very far along in doing so. Even at today's low price for crude oil, we've already seen peak use, and demand is fading year by year now, and Tesla progressing rapidly to making electric cars just a better bargain in pure costs, closer all the time.
But in a way the OP is useful -- it's good to ask nominal 'Christians' what makes them oppose knowing the reality of man made global warming. Perhaps someone might think more about what real faith in the way Christ meant is, so different from a mere tradition or group identification.
@Caliban