Some ideas:

Lots of New Republic builds aren't very dependent on CEs. Say something like Han Solo GH or Kyle Katarn JBM, Mara Jade, Kyp Durron, Anakin Solo, Ganner Rhysode, and Dodonna. Only Dodonna has a CE, and it doesn't matter too much against Old Republic if you don't have it.

If you do want to play Commander Effects, using Pallaeon in Imperials gets around Bastila. You're safe from ABM within Ysalamari.

If you're seeing lots of Old Republic, Vong become a strong option. Nen Yim's bonuses are Special Abilities, not CEs, so they're not affected, while lots of Vong also have Force Immunity.

My playing of Imperials dropped off because I struggled to think of squads other than black and blue. Maybe I will look into that more. I also don't pay Vong much, but I will be doing it more with the new guy and his door busting bombs!

I agree with TheHutts as well. The majority of NR consists of self-suffiecient unique beatsticks, which can hold their own with or without CEs (besides, NR only has two commanders -- Leia JK and Wedge).

YV is also a good choice. A ton of SA's that benifit each other, and with the addition of the War Coordinator and the fact that most of the YV have Force Immunity, Bastila + other jedi/sith shouldnt be a problem.

Which brings up another point. Who was the scourge of the jedi even in the old days? The Sith. Many new additions of the Sith are becomming powerful threats with the right combos. While some commanders may lose some of their potential (such as Bandon and Exar Kun), they are still formidable threats. Ex: Run Kun with a speeder bike, and when Bastila uses her ABM, run the bike up to her, swap Kun in via TE, and attack her and cancel her ability. Similar to NR, the Sith's beats are very self-sufficient, running any of them should work well against OR. Top choices that come to mind are Talon and especially Zannah.

However, for Imperials, you cant quite run them in the same way. Since many of the classical Tier 1 and 2 Imp squads were CE-orientated; using them wont work anymore. Classical combos such as Palpy-Potty + VAU and new Thrawn B&B lose their effectiveness. However; the addition of Palleon provides an effective counter. Him paired with the old Thrawn provides a double bubble to protect against Force Abilities/Powers. And if you dont play Bastila; you still have the flexibility via Palleon to swap GA Thrawn for the new one or a powerful Vader for an old one. The cool thing about Imps is that they have a bunch of options.

As a general rule of thumb; heres a few tips to counter Bastila:

Always have a door control. This is a given regardless of whether Bastila is on the field or not; but is especially important here. It would suck to come close to killing her; than having her get locked up by Atton J. Rand.

"Runners"; as I like to call them. Something that can ignore enemies and get to Bastila fast. The most ideal is Dark Woman; but other options are sufficient; such as the swoop bike; Basilik (yes; the Basilik :p ), and Snowspeeders. Not many options; but they really help in disrupting Bastila's ABM; assuming you can get to her.

Characters such as the Czerka (as mentioned before) that boost allies via Special Abilities and not CEs. Even abilities such as Empathy or Synergy are self- or ally-boosting affects that make a great impact in squads.

Lastly; Reserves are a good choice as well. These allow you to customzie your squad a little after seeing your opponents'; which is why a lot of champs have Lobot in their regional or national winning squad. Just dont bring in x10 Mousies. Thats just being a jerk :p

Hope that helped...I rambled on quite a bit.