Not at all.
>When it's done by whites – or actually, anglophone whites – it's not even called immigration
It's called "gentrification", and it's bad according to the left.
>When others, i.e. non-anglophone non-whites, do it, that is.
When non-Whites do it it's openly celebrated, and more is called for.
You seem to have got it backwards.
But when white anglophone people do it, it's not only normal, but so extra-chic that they're not even called immigrants but "expats". Pointing out that this is a bit of a silly level of privilege is hardly "Anglophobic". (On the contrary, your claiming that it is comes off as rather like bigoted white Americans wailing that "It's really the white man who's oppressed nowadays" when their privilege is pointed out to them.)
And as a born and bred lifelong European I don't think I'm particularly "Europhobic" either.