All the frustration you are going through, Beepers, is about the culture of the workplace, and it's not related to public service vs private enterprise (the same shite exists in both).
I have a theory that's not worth the ****-wipe it's written on, but still floats my boat:
1) Culture exists wherever 2 or more people interact.
2) Culture describes the commonality of those involved.
3) Where a culture is not defined / guided, it will create itself, and it will undergo a process of declining standards until it reaches the barrier of the lowest common denominator (ie where one or or more of the participants goes "Wtf!". Without further intervention, that is where it will stay, continuing to test that bottom-feeding barrier, unless the Resister leaves.
4) For a culture to rise from the muck, it needs reference points that help describe it. In a company, these are usually stated as values.
5) To fight back as an individual, testing actions / inactions / interactions against those values is the power tool, as everyone is contracted to adhere to those values. Hold people to account for transgressing the stated values.
6) If TAFE don't have defined values, you are foobarred. Best to find a culture that is a better match for your own value set.
7) Do what's right in your head.
