At a purely structural level, I believe mathematics can have subtle political implications. For instance, statistics is concerned with patterns in the aggregate. Structurally, this has resonance with utilitarian philosophies ("the greatest good for the greatest number") and for big government approaches to problem solving.
On the other hand, one of the tenets of chaos theory is the large impact of small individual changes. Structurally, this has resonance with existential philosophies (the power of the individual) and with libertarian political impulses.
Going further back, we can draw a connection between the idealism of classical geometry and the corresponding idealism of a political system like Plato's Republic.
Of course, these correspondences are not exact or inevitable, but they do show that even mathematics is not entirely politically or philosophically neutral. And of course, we can further note that the world of mathematics --in terms of what gets attention, and what doesn't --is also inevitably political (as is every other area of human group endeavor).