I have no doubt that Albus Dumbledore, had he been a Muggle, should have been a Liberal, then an SDP member, then a Lib Dem. He had his Grindelwald moment, and then went back to schoolmastering.
Harry had his Grindelwald moment, and then remained at the sharp end.
There is no certain canon - there are persuasive deductions, but no declarations from on high - as to whether the Aurors are more like an Army, an intelligence agency, or the Old Bill. It really doesn’t matter to this particular point. Given the choice, in these circumstances, of deciding whether a senior officer of Aurors should be, in Muggle terms, a Tory or a Labour supporter, the better wager is the former. (If you are required to make him PM, rather than simply an MP, you really cannot make him a Lib Dem. There is simply no foreseeable future in which, after a General Election in the Muggle UK, the Lib Dems shall go home and prepare for a majority government.)
Yes, there are Brian Paddicks. Yes, particularly in the politicised Met consule Tony, and with ACPO succumbing, as public employees’ unions always do, to rent-seeking, there were Ian Blairs. But the odds are that a senior officer of the Forces, a spymaster, or a Chief Constable - and being head of the Aurors is congruent, surely, to one of those three things - shall be, on retirement and unmuzzled, a Conservative (or a Crossbench peer, although that means never being PM), and at any rate not a Lib Dem and not Labour. See also, Lord Dannatt, Lady Neville-Jones, Lady Manningham-Buller, Dame Stella Rimington, Lord Byng, Lord Trenchard…. In American terms, what was Wesley Clark’s one selling point as a Democratic candidate for his party’s presidential nomination? That he was one of vanishingly few senior officers not to be a Republican.
And so, in Bezique, I made Harry a Tory in the Muggle world; on other occasions, a Conservative local councillor when dealing with Muggle neighbours. I think this plausible. You may not. I should be delighted were others to remix these ideas and plausibly make him otherwise. And a criticism that, This is not convincing to me, and these are the reasons why, is perfectly valid and perfectly welcome.
A complaint, however, that this is Simply Impossible, Because Conservatives Are Vermin, is rather less suasive. (It is also the sort of thing that leads talented people, some of who are otherwise morally decent as well as talented - the two are not coterminous on a Venn diagram - to do such things as to criticise others’ celebrating the deaths of, oh, Pol Pot or Ceausescu or Saddam Hussein or UBL, and then to dance in the streets when Maggie died.)