You're totally right of course and I think it's pretty shocking that military personnel aren't aware they are broadcasting their location out to the web. Complete opsec failure.

They are, they just don't care. The State Dept will likely issue a ban on their facilities which personnel will adhere to. Other military installations like Special Forces bases or regular Army bases overseas probably will issue a memorandum ("Be Vigilant!"), but I predict they won't stop using the devices. State Department facilities are the only places that they try to hide from others. Not that people and equipment are operating out of them (because that's impossible), but that they are State Department facilities to begin with.

These are most most certainly not patrol routes, but routes taken by people in their off duty time or in mandatory fitness time.

Well, a route taken regularly at 3 am is almost certainly not someone taking an off duty stroll. I do not know if you can readily figure that out from the data available through Strava. But if you can, this is bad.

How can you be so sure? Patrol shifts are normally rotated to prevent exactly that among other reasons, while someone having a regular non-patrol late shift (or early) and doing his exercise regularly at 3 am is also not unheard of.

I did do some guard duty. The bases I was at were dead silent in the middle of the night.

You might be able to, but even then it is more likely to be a person doing exercise on a device with the wrong time zone than it is to be someone on patrol.

To reiterate: Strava isn't always on. These are activities people have actively chosen to log. The chance of it being someone out on patrol is... not high.

Having to actively log the data is interesting. I agree with your conclusion there.

However, GPS is primarily a very high precision time signal, from which the current location is reconstructed. Basically, a properly designed software would do the proper time zone adjustment based on that, so the data should ideally be in local time everywhere without exception. Everything else would be a bug in my book.

OK, but that isn't how these devices work.

Source: I've used lots of them and it's a real pain in the ass.