The people in the unions, and the leaders, are not "pro government spending" they are pro "the government spends money on me" it is a small but important difference.
The government is a massive organization. Ignoring the cynical interperatation, it is entirely reasonable to think that there are some legitamate areas for the government to spend on; as long as the worker is in one of those areas, there is no dissonance.
Alternativly, someone could think 'I want to work in industry X. I think X should be privatised, but since it is government run, I'll work for the government'.
Further the cynical answer of 'the government shouldn't be spending so much money. But as long as they are, I should get some' isn't that bad of an answer