Howcome there's no Conservative anti-fascist movement?

Typically with good grace and an acknowledgement of the victors' efforts.

you could say that about any job really. If you don't do what you are paid to do, you get fired, full stop.

In some jobs I'd agree, but the logical of @T.R 's point is that soldiers are in some position able to judge and influence the decision to go to war.

That's simply not true and your average soldier has no more insight into the political purposes of said war than anyone else, arguably less in fact given the indoctrination involved in serving.

No, see, war being outside your experience, combined with America's pretend worship of the veteran is supposed to gaslight you into shamed silence.
Conservatives think that's how you win arguments.
Blasting the opponent with the right quantity of the right emotions, and/or manipulating the mob against you.
Don't you watch Fox News?

You are supposed to watch Faux news? I thought it caused brain damage.

No, brain damage helps you watch it more than 20 minutes.

Is it because some conservatives are fascists themselves, and other conservatives think they can use fascists to win elections without it blowing up in their faces?

It’s because conservatives end up being useful idiots to fascists. The fascists do share some small degree of agreements with normal conservatives, nothing actually fascist though. So they use that to get close and use them against their mutual political enemies on the left. They gain power, purge the left, any other group they want to get rid of, and any conservatives who aren’t on board with them at that point. This happened before, it’s happening now and will likely happen again at some point. It seems to be a cycle that repeats because conservatives would rather side with fascists than the left over anything, including saving their own lives and keeping their country a democracy.

I know no conservative will believe that, but you have just as much to lose as the rest of us and you could actually stop this in it’s tracks.

the average soldier can try to influence how wars are fought - how doctrine can be changed, how equipment & weapons & training might be improved, etc.
As for "indoctrination" that might have worked on 18 year old farm boys decades ago. These days not so much. I am no more "indoctrinated" than Anc, Marso, or Shirogayne and I served more years than all of them put together. The movies might show an indoctrinated military (usually to drive home a ham-fisted political point) but soldiers/airmen/etc. are more hip to what is really going on than a lot of civilians realize. But they have to get along because they are part of a team working together with a damn big responsibility so they "play the game" like everyone has to.

That said I am somewhat indoctrinated into thinking that military members in general are "smarter than the average bear" compared to civilians.
And by smarter I mean any random 100 military (active or retired) are stronger, leaner, healthier, more disciplined, more tenacious, and more focused than any random 100 civilians.
This is because anyone can be a civilian - we are all born that way. There are no standards you have to meet & maintain to remain a civilian - but there are standards & personality traits needed to serve successfully in the military.

An hour of every day doesn't go by when I don't use skills learned in the military that I apply to civilian life. Some are life skills, some are tactical skills, some are neither of those.
I see this big time in my son, who only served one contract but it did him world of good.

Influence how wars are fought absolutely, but not if they are fought or why.

I agree that in some regards ex military types tend to be above average, although that's not across the board. We're very poor over here in our after care standards for ex military and a lot of our veterans end up unemployed, in prison or homeless which tends to load the dice against them to say the least when paired with the general tendency for military qualifications to not be recognised within the civilian domain.

I'm not sure we're using the word "indoctrinated" the same way here, but I'm picturing how the situation would typically play out if someone were to tell a group and service personnel they were the bad guys in Iraq to their face. Not to put a fine point on it I've ad exactly that conversation more than once with ex servicemen.

Ours tend typically to agree, there was a strong anti war sentiment within our forces, but Americans I've spoke to tend to be quite hostile to that pov and you may have noticed I have a tendency to speak my mind....

It's also worth bearing in mind that the word "fascism" doesn't actually mean what a lot of people seem to think it means.

It's commonly understood as nationalist to the point of xenophobia, to the point of bigotry, to the point of violence, to the point of genocide.
Also, paranoid authoritarianism to maintain the status quo among the citizenry.
Conspiracy myths usually heavily feature in its psychology.

Yet somehow a left wing anarchist group seem to have recently earned it as a descriptor.

People seem to use it for any group or ideaology which is harmful, violent or just not to their liking.

Yes, very much this. It should mean authoritarian (and technically NOT totalitarian), violent government by a small group of capitalist/corporate owners. But it is often used in a hundred different ways. It's also originally a self-descriptor, so one could argue that anyone who doesn't call themselves fascist isn't fascist, although they might be similar to fascists despite themselves.