I don’t know if anyone needs to hear this but I use this all the damn time.
So when you’re doing the cross you stick blue and green opposite each other, and red and orange opposite each other.
I find that I’m rubbish at the order they go in. I know it’s Blue Red Green Orange but sometimes I’ll go blue orange green red by accident.
As long as you have the opposite colours, well, opposite each other (blue-green, red-orange) and haven’t royally fucked it up (Blue green red orange) then you can just do this.
Get your wrongly aligned middle slice and move it into the yellow layer with an M2, then spin them the opposite way around with a U2, then put them back with an M2.
Thing is, you don’t have to do this immediately. You can actually do the whole of F2L first, then flip em afterwards. Meaning instead of getting in a bit of a panic about having done the cross wrong and trying to figure it out you can say to yourself “Oh yeah, better do that alg when I get a chance” and do it when there’s only yellow edges in the M slice partway through F2L or leave it until you’re done.
Also, you don’t necessarily have to flip the bad 2 edges, you can flip the good 2 edges if you notice before you F2L and just realign your white slice so the cross matches.
TLDR: M2 U2 M2
Similarly, as a child I discovered R2 U2 R2 U2 R2 to swap two F2L edges (RF and RB.) In the rare instance I pair the wrong corner and edge together, this ends up being faster than fixing it.
I read this wrong initially and thought you meant the corners. I tried it, didn’t work. But then I tried it with a completed F2L and realised I’d switched the edges, came back to tell you it works but for the edges, then reread your comment…
Yeah this one is pretty great, thanks!
Adding to this, M2 U2 M2 swaps the 2 opposite edges in the top layer as well as the 2 opposite cross edges. So, if you mess up your cross, you can do the entirety of F2L and OLL, then do M2 U2 M2 before PLL, also swapping 2 top edges in such a way that you “force” a good PLL (IIRC you can turn a G perm into a J perm by doing this).