I was hoping one of you nice people would have the answer to this question! When using the move Foul Play against a physical attacker that has been burned, Intimidated, Charmed (essentially, anything that drops attack stat), does the move lose it's effectiveness? I know it gains effectiveness if the opponent has boosted. I've searched common websites, but haven't seen mention of it.

Im gonna have to say yes to your question, mainly cause it does say in the detailed description that it does take Modifer's that are affecting the opponent (both positively and negativly) into the calculation.

I did try to confirm this for you via the psypoke's damage Calc, but I couldnt find Foul Play in the Calc, Ill keep looking just so you can have a definative answer.

EDIT: Yes, I can say with 100% certainty: If your opponent's Attack stat is affected with a Negative Modifer, Foul Play losses it's effectiveness.

From the Pokemon Showdown Damage Calc :

+1 4 Atk Klefki Foul Play vs. 252 HP / 0- Def Abomasnow: 136-160 (35.4 - 41.6%) -- guaranteed 3HKO
-1 4 Atk Klefki Foul Play vs. 252 HP / 0- Def Abomasnow: 61-72 (15.8 - 18.7%) -- possible 6HKO

As you can see with Abomasnow at -1 Takes twice as long to KO than one at +1. (at -6 It literally says "worst move ever").
If you Plan on using Foul Play, I highly suggest you use it in conjuction with Swagger (if your using showdown rules, please keep in mind that swagger is currently in suspect testing).

That was fast! Thank you so much for going the extra mile and giving such thorough feedback! Hats off to you!

One thing you forgot is that if the opponent is Burned, it will not lose attack power, however if the user of Foul play is burned it will cut the power in half.

Is this actually true? I've been concerned about this recently

Yes

0- Atk Klefki Foul Play vs. 252 HP / 0 Def Abomasnow: 81-96 (21 - 25%) -- 0% chance to 4HKO

0- Atk burned Klefki Foul Play vs. 252 HP / 0 Def Abomasnow: 40-48 (10.4 - 12.5%) -- possible 8HKO

0- Atk Klefki Foul Play vs. 252 HP / 0 Def Abomasnow: 81-96 (21 - 25%) -- 0% chance to 3HKO after burn damage