@coldjoint,
coldjoint wrote:That is all it took to discharge this soldier?
Yes.
Laws are laws, like civil servants, members of the Royal Family and broadcast journalists, serving soldiers and other military personnel must remain apolitical. (Posing with Theresa May or Jeremy Corbyn and chanting their names may have incurred just as strict a punishment.)
Additionally, members of the military have been warned on previous occaisions against affiliations to the EDL. (In 2017, two serving British soldiers were charged with being members of the banned organisation National Front.)
Besides that: the Royal Army was alrteady investigating before the Muslim Council of Britain "complained" (easily to notice for those, who can read dates).