Well to start off, One of the videos,(the crutches kids video) is actually Dutch. The "kicker" was a normal, white, Dutch national, https://www.geenstijl.nl/5139660/lol-real-donald-trump-retweet-dumpertvideo/ . so it's #fakenews (Dutch site Dumpert.com posted the video a few years ago and users identified the kicker, who got arrested) This gives a direct window into where Trump is getting his information from and basing his worldview on..... He didn't just read it, no he felt the need to take this as a fact and share this information with us all.
Marginal / minorities or not, BF is an UK extreme right-, active political movement none the less. With ties to neo Fascism and very extensive anti-Islam ideas, which makes this very, very awkward. I understand you and fellow North-Americans take this as lightly and popcorn while your popular media runs dramatically wild, On a US scale this is a marginal "scandal" I agree. But it's not taken so lightly in regards to your foreign standings in UK/EU, causing political friction for UK PM May and sowing doubts amongst your allies. Mind you, we do tend to take minority political organisations related to "neo fascism" a tad bit more seriously over here then in US due to our recent history.
I don't think Trump actually realised that this was a tweet from an account related to a political party, he probably saw "britain first" and thought it catchy and similar to him. Still ignorance is no defense and worrisome by itself.
I have looked at them before. It is a tiny group that has radical, but non-violent views, that they are pressing through democratic means, and protests.
It's a popcorn moment. Things are good if that's the worst they've got.
It does get big press though. Because it rattles people like you (with good cause). But it is not a significant factor outside of the media, and only has any relivancy because of the same media that is promoting and profiting off them.
Here's an article that puts it in perspective.