What does 打着 mean in 不能打着传统文化的旗号去否认简体字?
'打' in '打着旗号' means 'to display/ to hold up'
打着 means 'displaying/ holding up'
旗号 (flag/ banner) is a metaphor for 'claim; declaration'
More examples:
(打着)少林正宗的招牌 = (displaying/ holding up) signboard of authentic Shaolin
(打着)燈籠 = displaying/ holding up lantern
(打着)雨傘 = holding up umbrella
(打)手勢 = (display) gesture = to gesture

I'm not sure if 打 or 打着 (is 打着 a word here or 打 + particle?) has the positive or negative connotation in this context to begin with... It is likely 比喻 in this context.

打 is the verb, 着 is a particle that indicates 'on going' status of the verb. There's no positive or negative connotation on the verb 打 (displaying/ holding up) itself
打燈籠 and 打傘 are common terms that use '打' as 'to display/ to hold up'

&quot;不能打着传统文化的旗号去否认简体字&quot;
&quot;Should not holding up the banner of 'Traditional Culture' to dismiss simplified characters&quot;

Side note: &quot;和尚打傘: 無法無天&quot; - &quot;Monk holding up umbrella: no law (hair) no rule (sky)