Uses of V1 sentences
In German, independent V1 sentences (i.e. sentences with the finite verb in first position) are used to form yes-no questions.
Hast du meine Brille gesehen? – Nö.
Have you seen my glasses? – Nope.
Subordinate V1 clauses function as conditional clauses.
Hat der Minister gelogen, muß er zurücktreten.
Wenn der Minister gelogen hat, muß er zurücktreten.
If the minister lied, he has to resign.
Some people claim that the conditional use is derived from the yes-no question.
Hat der Minister gelogen? Dann muß er zurücktreten.
This claim matches with the fact that conditional V1 clauses cannot be postponed.
*Der Minister muß zurücktreten, hat er gelogen.
Der Minister muß zurücktreten, wenn er gelogen hat.
Construction in question
Let's look at some examples.
Sicherlich gebührt der Defensive großes Lob, war es doch bereits das dritte Spiel ohne Gegentreffer.
Surely the defense deserves credit, because it was the third game already without conceding a goal.
Früh fanden aber alle ins Bett, war es doch ein anstrengender Tag.
But everyone was off to bed early, because it had been a trying day.
Sein Rücktritt war abzusehen, hatte er doch das Parlament belogen.
His resignation was to be expected, because he had lied to parliament.
As the translation indicates, postponed V1 clauses are interpreted as causal.
Note that the V1 clauses need to contain doch. This makes them different from sentences with causal conjunctions, where doch is omitted. Duden actually has a separate entry for this type of doch (Bedeutung 2: Link).
Sicherlich gebührt der Defensive großes Lob, weil es bereits das dritte Spiel ohne Gegentreffer war.
Sein Rücktritt war abzusehen, denn er hatte das Parlament belogen.
Causal V1 clauses belong to written language. They hardly, if ever, occur in spoken language.
Sentence in question
The sentence in question has one additional complication.
Alle möglichen und unmöglichen geschlechtsspezifischen Diskriminierungen sollen aus Sprache und Leben der Grünen verbannt werden. Glimmt da nicht vielleicht sogar ein winzig kleiner Hoffnungsschimmer für alle Männer mit? Galt doch die Bezeichnung “Depp” bislang ausschließlich ihnen.
This is metacommunicative causality. Compare:
Die Frau lügt, weil die doch total nervös ist!
That woman is lying. She is so nervous!
The weil-sentence can be interpreted as giving a reason why the speaker claims the woman to be lying (as opposed to giving a reason why the woman is lying).
And this is exactly how the V1 sentence in question is interpreted: As giving a reason for why the writer believes that gender-neutral language carries "a glimmer of hope". Note that the writer is being ironic, though.