Wow that svcks.
The only outfit bug I've run into is where some outfits seem to be randomly locked to certain sixes. But I know its a bug. Like how my male dwellers cannot wear the engineers outfit or the soldiers outfit, only the females can. Yet my buddy Mango (a guy) comes back from exploring the wastes wearing an engineers outfit. I figured the bug was fixed, so I unequipped it from him and tried to re-equip it to confirm. Instead I couldn't re-equip the outfit, though it was in my inventory. I ended up handing the same outfit to one of my female dwellers.
Another outfit that does this is the royalty outfit, except the problem is reversed. It only lets males wear it, no girls allowed. The final outfit I noticed this on was the Librarians outfit, though I kind figured from the outfit picture that it was going to be strictly girls only anyways. (it had briast lumps in the pic)
Anyways back on topic: Have you checked your inventory? The button in the menu that is basically three boxes clumped together? Because if you can see the outfit in there but it has a dotted border, it means you MUST build more storage spaces before you can access it. (a bug in itself i think, letting you go over your max inventory amount) If you do see it and the border is solid, try equipping it on someone of the opposite six than the person you're trying.
As for changing outfits in the wastes, explorers will auto equip outfits or weapons that are "better" than what they're currently using. What the devs define as "better" is debatable though. If im wearing a +3 endurance suit, please don't take it off and put on something that has less endurance, even if it has other stats. Anything besides luck, endurance, and strength have no bearing while exploring, so removing my wastelanders gear (+3 endurance) for an engineers outfit (+2 endurance, +1 luck, +2... Intelligence?) seems to be counter intuitive.
Infact, being allowed to swap outfits on the fly sounds pretty handy! Wear a massive endurance booster to get out far enough to find the good stuff, then put on a +7 luck outfit and reap the rewards!