Its a difficult topic and not one that's easy to summarise in short posts on a football forum.
Obviously what your grandma went through was racism. Of course white people can be subject to racism. White people in the UK who have other heritage who I know also maintain close links to that heritage, in the same way brown and black people do. The Poles, Italians, Greeks, Portuguese, Germans, French, Norwegians, Spaniards, Swiss etc etc who are either mixed or have decided to make London their home all continue to consider themselves at least partly from that culture and maintain aspects of it. They see no contrast or conflict at all between speaking Spanish at home, supporting Atletico, cooking paella, going to Spain every opportunity they get to visit family, being loud and warm etc etc, with also feeling British and loving living in this country.
But let's be completely clear on something. Its horrible to even use this term but its sadly true. They can visibly 'merge' into the local population in a way that Somalis or Ghanians or Chinese or Bengalis will not. Ever. I know Bengalis who have been here 3 generations. 3. They are so integrated. English their first language, all uni graduates, contribute to the economy and society, love this country (its their only country), some in mixed relationships. Yet all terrified by the recent activity, knowing that the colour of their skin will always mark them out to some.
Lee Anderson was piping up recently about 'migrants' taking over a hotel in his constituency. Turns out they were a group of nurses and their families having a nice break. Imagine that. Brown and Philipino nurses doing the jobs that white people in this country no longer see as worth doing and they get aired out by this idiot as migrants, while attacks are going on around the country on migrant hotels.
Going back to the Argentina/France thing, it again kind of emphasises the point. France has white players of other European ancestry in their squad. Did they make it into the song? Or do they just disappear when the racism comes out to play?
People can be both proud to be British (and have been British for generations) and still eat jollof rice or curry or whatever their national cuisine happens to be. And be proud of both. That isn't a logical inconsistency.