Mathematics is not a field of natural science, but it is a science too. I've seen it classified as "structural science" before. It operates on the same tenets of the scientific method (which, in one sentence, can be described as "methodically testing falsifiable hypotheses"). The only difference to natural science is that the testing does not involve interrogating the physical world through experiments.
There is also "political science" and "social science".
There are also those who advance the premise that mathematics is empirical, but for the context of the discussion I'm not sure that either is relevant.
Mathematical "testing" can be described as deduction.
We can present math axioms, but can we present scientific axioms?
Science as a religion or science as an all encompassing worldview is unscientific. This is better described as scientism.
If you examine the premises of climate doom, you'll find unscientific presuppositions. There are also necessarily moral implications to the goals of regulating consumption and population size. It becomes even less scientific for cynics who question if the climate scientist's "experiments" and models are incentivized to necessitate certain conclusions.
These are items which are best disputed in their respective arenas. "Believe the science" doesn't tell us anything about morality or the ideological progenitors of the climate movement. It narrows the issue while mischaracterizing science as a system of belief which can inform us on moral matters or the historical record of climate doom ideologues.
Forget your scare quotes around science. Just go on facts. Do you not accept the idea that we have terrible wild fires in the western us, that we had sudden and unexpected very hot weather in the west? Do you argue that there isn't a big change in the climate from human activities? Do you want to argue that the measurements of carbon dioxide growing in the atmosphere is fake, or maybe doesn't really affect the climate?
Or do you disagree that the level of the sea is rising as frozen water at the poles is putting more water into the sea? These are things that are reality. It doesn't matter if you think I have impure motives about something, am I stating things that are reality? You have prevented no information that these things are not reality, you are just arguing about mysterious dark motivations of people who are pointing out things that are really happening.