Would you run this air filter?

If the next ride is going to be on a prepped track, or basically conditions that will make it about that dirty again, yes, that has another ride in it.    Now, if you know you're going to a total dust bowl that is going to coat the thing with a solid inch of silt.. then you might want to start fresh.

That shade of blue looks like Bel Ray oil.. so that's a plus.

Im borderline obsessive with air filter maintenance.  Ive changed air filters between motos before when dry and lots of dust.  If that was my filter and I went through the not so much trouble to remove to look at it, id change it.  I see your New Jersey and Ive used 2 filters at FOD on a race day when racing 2 classes.  I ran practice and 1st motos and changed before 2nd motos and only put an hour on the engine on those days.  

That's about at the point where I would change it if I was at home in the garage, however if I was at the track I'd have no problem running it. If you use good filters, good oil, and oil it properly, you shouldn't have any dirt pass through regardless of how dirty the outside gets. That filter looks like it meets all those things. You're doing it right. 

This.  People have this idea that the dirtier the outside is, the more the risk is that dirt will enter your engine.  Which is not true if it's oiled properly.  Actually, you probably run more risk of letting dirt in opening it up at a dusty track or knocking some in during removal.  

There's also this version of Twin Air dust cover.  This type you can oil and it will stop 90% of the crap from getting to the main filter.  I'll use these if I am doing a full weekend ride and remove it after the first day.

Performance is the same. They hold the fine dust and sand. NO OIL on the twin air only on the filter. Using three of these on a practice day when it's a dusty day. Some change every ride the filter on a race day (3 filters). Prefer to use three of these. Two laps and the sand is there.

If it’s ever a question, then the safest route is to just clean it. Cheap insurance 

If I looked down into the airbox and saw that, I'd probably run it. If I had bothered to remove it from the bike, like you did, I'd wash it. 

Mine gets cleaned every ride, no exceptions. I have 3-4 in rotation and bring clean pre-oiled spares with me on multiple day events. 
 

If I was in a pinch and saw that would I run it? Probably. But if it was already out of the bike I’d hesitate to put it back in, as the dirt on the outside could find its way inside during installation, especially on any bike where it goes between subframe rails and it has to be twisted around. Yours is obviously a red/white/orange KTM and this would be of less concern due to the airbox design, but still a concern.

I would if it was still on the bike. Trying to put a slightly dirty filter is a dice roll on getting dirt in the intake. 

I love filter skins. Filters last a long and makes it easier to clean them too. The twin air setup works good too. Keeping the larger debris off the filter. The non vented KTM airbox is pretty good at keeping larger debris out. Unlike my YZ250F, lmfao fuck that thing gets dirty unloading it from my truck. 

Would run that for sure. 

I only put clean filters in my bike.

If it's dirty like that I would take it for another ride but I wouldn't take it back in when it was already out. I don't want dirt to fall from a dirty filter into the intake.

Filter skins are one of the most underrated products. I notice no difference in performance at my skill level, two stroke or four stroke. I typically use them when I plan on riding back to back days and they definitely do the trick.