Fanaticism. A “dyed” Olympiakos supporter (βαμμένος Ολυμπιακός) is a die-hard Olympiakos fan, not an embittered Olympiakos fan. From the Triantafyllidis dictionary:
Λεξικό της κοινής νεοελληνικής
3. (μππ.) φανατισμένος οπαδός (πολιτικής παράταξης, ποδοσφαιρικής ομάδας κ.ά.): Είναι βαμμένος αριστερός / φασίστας / Ολυμπιακός.
Fanatical supporter (of a political party, a football team, etc): he’s a ‘dyed’ left-winger/fascist/Olympiakos [fan].
A ‘dyed’ fascist might also be rancorous because their ideology is not getting through; but you can certainly be a ‘dyed’ support when your party is in government, or your team is winning the championship.
EDIT: the expression is also in English: a dyed-in-the-wool Liverpool fan.