Trump re-tweeted the BF videos from a tweet by someone he follows, conservative polemicist and VE hero Ann Coulter. As has been pointed out already neither Coulter or Trump were likely to have had the faintest idea who BF were. Nobody outside Britain (most people inside, for that matter) has ever heard of BF; the fictitious threat to civil society posed by BF is a local and specialised study.
As for the content (which I haven't seen) apparently there are gays being pushed off buildings and one of a Dutch "immigrant" beating up a disabled kid. I've heard that the "fact-checkers" have pointed out that the thug in the latter video was not in fact an immigrant, but a Dutch-born Netherlands citizen. Ho, ho, ho! "Read my lips: no new taxes."
As for BF inspired crime, I'm reminded of the Manchester police exercise which simulated a terrorist attack when the guy playing the terrorist shouted "Allahu Akbar!". The police had to apologise because the phrase was an unfair slur on the moderate, peace-loving Muslim majority. Somebody killing you while shouting "Allahu Akbar", you see, has nothing whatsoever to do with Islam. By that logic Ellipsis' quoting Mair's alleged "Britain First" has nothing to do with BF and is a slur on all the moderate, peace-loving BF members.
Mikey's research has produced an attempted murder by a Pole who "the court was told" (I'd guess by prosecuting counsel) had once contributed to BF.
But, for the sake of argument, I'll take the BF atrocity count as one murder and one failed attempt. Now look at some other numbers. This from a Times article on a recent intelligence report (most of you will have seen this):
"Intelligence officers have identified 23,000 jihadist extremists living in Britain as potential terrorist attackers...
About 3,000 people from the total group are judged to pose a threat and are under investigation or active monitoring in 500 operations being run by police and intelligence services. The 20,000 others have featured in previous inquiries and are categorised as posing a “residual risk”.
The two terrorists who have struck in Britain this year — Salman Abedi, the Manchester bomber, and Khalid Masood, the Westminster killer — were in the pool of “former subjects of interest” and no longer subject to any surveillance."
Anti-terrorism efforts came under renewed scrutiny when it emerged that Abedi, who murdered 22 people when he detonated a suicide bomb among crowds leaving a pop concert at Manchester Arena on Monday, had been a former subject of interest to MI5.".
Britain burns; pass the fiddle!