The Free Commune of Gibraltar, was initially as some people have correctly pointed out, a Naissar Soviet/Kronstadt expy. After I offered to help with writing it, I looked into the history of the Gibraltarian labour movement. The main sources I used were "‘Reformers and revolutionaries: the battle for the working classes in Gibraltar and its hinterland, 1914-1921’", "Workers of the Empire, Unite", "Anarchy in the UK('s most famous fortress)" and a Spanish book named "Yanitos. Viaje al corazón de Gibraltar (1713-2013)".
From my understanding, the workers at Gibraltar (primarily Spaniards from Andalusia, but a lot of Brits as well) were extremely militant, particularly in the late 1800s, early 1900s. Though initially influenced mostly by Spanish anarchist trends, both British and Spanish syndicalism took hold around the 1910s. There were numerous wildcat strikes, as Spanish and English speaking labourers joined forces and cooperated. There was even a chapter of the CNT and the FAI established. By 1919 this unity between the Spanish speaking workers and the English speaking workers fell apart, at least in OTL. Not only did the British government start issuing some concessions, including democratic representation and better labour rights for Gibraltarians, the British Workers' Union also dispatched a representative name Matt Giles. Giles explicitly told the British labourers at The Rock to pursue more moderate organizing, in the whole "legalist" trend that was taking shape in Britain. He also explicitly denounced the Syndicalists, Anarchists and Communists among the trade unions of Gibraltar, and told British workers that they should not affiliate with Spanish speaking workers, and instead form exclusively English speaking unions. This pretty much killed the labour militancy and divided the workers. A while later Britain continued with its carrot-and-stick approach to mollifying the labourers on Gibraltar, until the radical workers movement was all but extinguished.
In KRTL, considering how much more radicalized the labour movement in Britain is, I thought it natural that the Gibraltarians would also be affected. As the wikia article says, the dire circumstances in 1925 lead numerous workers to repudiate Matt Giles instructions and to reform the multilingual alliance between Brits and Spaniards. There is also a much bigger influence from the British TUC and the Spanish CNT on The Rock, compared to in OTL. Its also questionable if Britain would offer the same concessions to Gibraltarians in KRTL, considering the hardline approach they've taken to other colonial entities which underwent reforms in OTL. Either way, even if they did, it would be too late. With economic decline, radical influence and a resurgent labour militancy, I do not think its unreasonable for the workers of Gibraltar, joined by the garrison, to declare themselves a commune. Trust me, British workers and soldiers have rebelled in way weirder places than Gibraltar. (Look up the Cairo Forces Parliament's mutiny in Egypt for instance).