I was a linguist as an undergrad - did no politics modules at all, but it was a top uni - and got in to an excellent university (top 10 for Pol) to do my MA in Pol, no questions asked. I was in a class with people who had done International Relations, Politics, and Pol theory as UGs, but it was not hard to catch up... and I got a distinction. My PhD is also in heavy Pol Theory and Philosophy.
What I had was skills that helped me to learn quickly, and the uni where I did my MA recognised that.