This is a misleading comparison.
Political parties are not supposed to be neutral. They unequivocally
represent the interests of their donors and membership. For instance, the
Labour party in the UK is meant to give the trades unions a political voice.
If they were "neutral" they would represent very few people. Even so-called
'centrist' groups are usually right-wing authoritarian in policy, claiming to
support "liberalism", itself a relic of 19th-century laissez-faire
ideologies.
A nonprofit charity or organisation is meant to represent the stated aims,
rather than the beliefs and ideas of the groups bankrolling it. In practice,
it is important to acknowledge that some charitable organisations are
corrupt, but reputable charitable organisations shouldn't do this. If they
did, then people should not support them. The FSF represents free software,
and that is it.