Why is it because it's a government? Why do you think that simply moving the organization from the government to a private organization would somehow make it less political?

Do you think that politics can somehow only exist in government? I disagree, politics play significant part in any human endeavors, see for example office politics, corporate politics, etc.

Private organizations are patronized by market capital -- though more importantly, as individuals condemn it afoul, not patronized. The same isn't true for the state, of which there is only one, and operates as winner-take-all.

Not necessarily. They could have donations made to them for political or ideological reasons and stay in business this way. Plenty of companies have expressed political leanings as part of their marketing material in order to capture different customer segments more thoroughly.

Private professional organizations are never patronized by market capital. How would that work anyway? They're professional organizations, they don't make a product. They're organized as a non-profit of some sort.

The problem here is that this gentleman is speaking truth to power, and power doesn't like that very much. The professional organization being governmental, or having a government-granted monopoly, versus being a private organization, is basically irrelevant. The organization being part of the government usually grants additional public oversight, not less.

At least some of his issues were from other individual P.E.s filing complaints against him. That's the sort of thing that can happen in any organization, governmental or not.