The judge said she did not think "the complainant was as 'alarmed and distressed' as they portrayed themself to be by these messages and this course of conduct".
She also ruled that "the complainant was not giving entirely truthful evidence" during the trial in September, while Linehan was "generally a credible witness".
He has been fined £500 and ordered to pay costs of £650 and a statutory surcharge of £200.
During the trial, Linehan told the court that knocking the phone was a "reflex response", and that his life had been "made hell" by transgender activists because of his views about gender identity.
Judge Clarke said it was "not for the court to pick a side" on the "continuing debate about rights of individuals regarding their sex and gender identity".
She explained that the prosecution used female pronouns to refer to the complainant during the trial, while Linehan's defence used male pronouns. The judge said she had chosen to refer to Brooks using "gender neutral pronouns and as 'the complainant'" in her ruling.
https://feeds.bbci.co.uk/news/articles/cjrj4520rrwo
(Posted as much for seeing how the BBC is reporting, as for the Judge's comments.)