"It seems much too tainted by Politics to actually remain objective, which is a critical element of good Science."
Given the fact that you only come into contact with the pop version of economics, that view is understandable. But the economists that actually write research papers and not just write op-eds to newspapers do not start their research with a question "how do I support my political views with suitable evidence". Sure, they exist, but that applies to climatologists as well. The share is higher than it should be, especially among those that only want they bacheor's degree, but those who act this way are not those who win Nobel Prizes and develop the discipline.
Also, I make a claim that if mathematics is a science, economics must be a science as well. Much of mathematics is, how to call it, "pure" mathematics, i.e. it has no inherent connection to real world. Someone could claim that "pure" mathematics cannot be science since science requires testing against evidence gather from nature. I call bullshit. Evidence from thought experiments counts as well. If I create an imaginary world that obeys certain consistent rules, I can easily derive meaningful evidence (observations?) about the said world from those rules and shape a falsifiable theory about the world from it. This clearly follows the scientific method, since I use objective evidence to form falsifiable theories. That's how much of pure maths work and why it's maths.
Consider the example of economics. You construct an imaginary world which follows certain clear rules. You then introduce further elements to this world and observe how an agent following the preset rules interacts with it. Since you know the agent has to follow the rules, you can create a theory predicting his behaviour. Still, the theory you formulated might be proven wrong if further research shows you didn't take into account evidence that could be gathered somewhere else in your imaginary world. The process is scientific as well.
The problem is the goal of economics isn't in this basic research but in predicting he behaviour of humans. The imaginary world is thus reshaped to more closely resemble our world. Sadly, this process has serious limitations which seriously compromises the scientificness. Economics has theories for worlds with exogenous money and for those with endogenous money. But what we really want to know is whether our world has exogenous or endogenous money so that we can act accordingly. However, this can be only resolved via evidence gathered in our world - and this world doesn't obey the rules we set for our imaginary world of homo economicus. Yet our only tools are those of the imaginary world, so we pretend our real-world evidence is the imaginary world evidence and feed it into our models. This, of course, creates results that are hardly unshakably scientific - which is why it is notoriously difficult to discard economic theories. Not to mention the multitude of economic schools, some of which operate in the imaginary world with the same rules but introduce different elements into it, while others have their own imaginary worlds. This is in itself hardly problematic but again, since we do not study these worlds an sich but because we want answers to real-life questions, the bitter political fights arise. So economics is inherently schizophrenic since when it's in its most scientific form, its practical value is severely limited, while the applied economics has the highest real-life impact but is hardly scientific.