You're able to shrug off most of their Psi Attacks if you come prepared - with psi screening and psi-buffing gear. If you don't, there WILL be trouble. That's why the Star Gods proper will never attack your hideouts unless provoked, it'd often amount to instant game over.
In normal missions, the impact of combat stress is unnoticeable for me - there's additional pressure but no real problems. Also there are many outfits that decrease the rate of combat stress, Bravery is also a major factor (you lose 14 Morale each turn with Bravery 10, and only 7 with Bravery 80). This was done to add human frailty element into the game, and to slightly punish campers (with the right gear and high-Bravery gals, you can decrease the combat stress to almost 0 - it just forces the campers to prepare more thoroughly. However before you get the hi-end gear, you're paying with armor protection). It also forces those who rely on 'superfast' gear to actually act swiftly. Said gear was buffed a bit TU, Stamina and Reaction-wise to compensate.