Fair play and completely understand your point of view.
From a personal standpoint the term mongrel has always been associated fondly with Australian soap opera. The Jewish mates i have been out on the ale with tonight (admittedly a poor survey of one) had never heard of the term in that context either.
I make no bones about it. I love saying flaming mongrel. Well i hadn't said it for several years but now my love is rekindled.
I guess it's all about motive. I profess myself ignorant about that term in that context but if it was offensive to people I'd shrug my shoulders and move on. If people use a term in knowledge and with intention to cause distress or offence to someone then i feel bad for them and hope they can become more kind.
I think you are correct in the context. My position is not that all Kopites are Nazi sympathisers (in spite of how they caricature what is said).
The context you seem to be using it in is a very generalised manner and as such is essentially meaningless.
However when it is directed at another particular group of humans (as they are increasingly doing towards Evertonians) it takes on a different context to me. It's saying a whole category of people are inferior to the "thoroughbreds" (which I presume in their heads are themselves) though of course they are about as close to Nietzsche's "Übermensch" are the likes of Ernst Rohm, Goebells and Hitler were to being a higher human specimen. It's a nonsense but it easily leads to a slide towards biological determinism (which is of course the key differentiator between mongrels and pedigree).
Whenever you try to have this discussion with them it just tends to lead to further abuse, people mischaracterising what you are saying, Nazi apologism (some disgracefully saying the Nazi's never actually practiced these ideas) or in some cases them using the phrase an awful lot more often (particularly when they realise the in laws Jewish background, which seems rather odd).
Either way, the lad tweeting ought to do better than blocking people highlighting it while generally relishing the ability to wind people up. They seem to have developed a particular love of Geordies recently too on the back of them singing "feed the scousers" all game and then using misogynstic language in public. I wonder what has led to them suddenly finding such an admiration for Newcastle fans?