Meanwhile, Discourse moved to Crowdin to handle interface language translations. I can’t find any reference to formal and informal variants but they do have regional variants. I wonder whether these regional variants are fixed by the system, or whether project admins can create new ones. If admins can, then it would be possible to create i.e. Hungarian (Informal). The software even can fill automatically non-translated strings between variants, so translators only have to focus on the sentences that differ with formal and informal.
If this process would technically work, then creation of formal/informal variants could follow the same process than the request for new languages.
As a speaker of various languages with formal and informal versions, I agree with everyone requesting this feature here (disclaimer: @Tgr and I come from the same project). Finding an English equivalent is hard, but imagine that the Discourse interface would be addressing everyone with the tone and the register of a servant in Queen Elizabet’s court. 
What is bothersome about the current “process” is that there is no common standard. Different languages have been translated to formal or informal depending on what the first translator(s) decided to do when they started translating.