In space combat, how do you disable shielded targets?

It is possible to destroy them. It's just hard.

I had been curious about this as well and when I hit level 26, I loaded my ship up with a bunch of upgrades and went back to that starting mission, Balosar Outpost. You CAN blow up that shielded antenna on the bottom, and you don't need protons to do it.

When doing the mission, I saved a lot of my missiles for the antenna, and I launched missiles at it and fired at it whenever possible. On one of my last passes at it (probably put about 20 missiles in it, plus a lot of gunfire) it blew up and I briefly saw a bonus objective message appear in green text across the screen for destroying the antenna relay. Note that it was an "unadvertised" bonus, as I hadn't seen it in the quest log.

I was also able to do this on the Makem Te Assault against the shielded node on the destroyer, too. My ship is fully upgraded (for level 27) and it took about 30 missiles plus a lot of concentrated fire, along with the augment thing that has guns do more damage while shields regen slower. When it blew up, again I got a "hidden" bonus objective complete message.

Missiles are the way, for instance for cartel listening station you have to save and use almost every missile on the bottoms spire if you wish to destroy that (is a bonus bonus mission). Warning! If you destroy the entire station the game WILL crash! Hope they fix it :(.

They can be taken out by using the torpedos you get a lvl50.

EDIT: Targets that flash like that are heavily shielded. As near as I can tell, blasters simply have little to no effect (the only time I've seen different is in the shield generators on the Makem Te Assault) and they take a significant number of concussion missiles to crack, varying by mission and component.

For instance, the first tier mission frigates' shield generators fall to two missiles apiece, while at the later tier they require three hits; at the final mission some of the shielded hardpoints (which are also primary mission targets) take more than a full magazine apiece.

Proton Torpedoes, on the other hand, have a /very/ long lock time and will refuse to even start the lockon procedure against anything that isn't an appropriate target -- meaning capital ship shield generators, bridges and that bottom antenna of the space station -- but they will kill whatever they hit in one shot. Unfortunately, you can't fire a regular missile at anything that can be targeted with a PT unless the torpedo launcher is currently unloaded even if it would only take two concussion missiles to breach the shield generator...