Are sciences like physics relevant to social and political thinking? Arguably they are, not directly, but as they influence one's general view of the world - one's metaphysics, if you like.
Consider relatively recent developments in physics - particularly those relating to our clearer understanding of the notion of quantum entanglement, and the realization that information is physical and a more basic physical concept than matter or energy.
These discoveries and new ways of thinking allow us to reassess various older traditions of thought. Personally, I am led to look again with increased respect at philosophers like F.H. Bradley (a 19th century philosophical idealist) who, entirely innocent of mathematics and formal logic, articulated a view of the world in which everything was related to everything else, everything was ultimately inseparable from the whole. Schopenhauer (drawing on Indian philosophy) had a similar view. Spinoza was an important source for Bradley's thought - indeed there is a rich tradition of thinkers in this vein. Some were religious, others less so or not at all. The wholesale rejection of idealism by philosophers in the early 20th century occurred just when physics was beginning a revolution which would vindicate important elements of philosophical idealism.
I am not suggesting a return to philosophical idealism, however. Any metaphysics of the future needs, in my opinion, to be firmly based in physics and quantum information theory.
Issues of politics and society can of course be dealt with without reference to physics or information theory; but they cannot be dealt with in any comprehensive way without reference to religion. This is because so many Western institutions and ideas and modes of thinking are influenced so profoundly by Christian and classical (especially Platonic and Stoic) thought. Even people who don't think of themselves as religious continue to hold beliefs which derive directly from religious traditions. This applies to value systems (humanism could be seen to be a Christian value system) and also to more general ways of thinking about oneself. Religious ways of thinking (e.g. the mind as something different from the body) come naturally to us, whereas scientific truths are often counter-intuitive.
My views on science and my (very limited) scientific knowledge form the basis of my secular view of the world; and this secular view clearly affects my political and social views. Physics and information theory may not have direct applications to social philosophy, but indirectly - by helping to form a secular view of reality - they influence profoundly my social thinking.