Everything is political in one way or another.
Buried at the bottom of the article I linked, you will see what public health officials are worried about. Germany has a huge antivax movement. The vaccine won't save many lives if no one gets it.
Drug approval is always about trying to do the most good for the most people. Lots of people die from cancer while drugs that could help them are awaiting review. Without that review however, many more people would die.
The initial doses of vaccine will cover a small percentage of the population, and be exhausted weeks after approval. Whether the FDA approves today, on the 10th, or even Jan 1st will have no effect on when most people get the vaccine.
The UK wanted a PR victory, and they got one. I don't think that will lead to problems, but I also don't think it's a good reason to rush our review beyond the extreme speed it's already moving at.