zorro used in the benign way in which you describe your understanding of nationalism there is nothing wrong with the word, in is to be applauded particularly if it assists in the national community coming together for the greater good.
I am not using it in that sense.
Basically, nation means belonging together by birth or place of birth, and nationalism is concerned with people who are related by their place if birth. Nationalism in this sense is a socially constructed community which is to a large extent imagined by those who perceive themselves to be part of that construct (Anderson)
It is an imagined community because you can't possibly "know" everyone in that community. We have visual images such as the Union flag, or the Crown representing this nation.
So in this tradition it may be argued that nationalism should be defined as a political doctrine. For many nationalism as the objective is it achieve a mono-cultural state.
There are nationalistic groups, and the one that killed Mrs Cox is one, who work to ensure that the state includes only those who seem to belong to their definition of a nation. You could describe this as ethnic nationalism, as opposed to what you are describing which is civic nationalism.
We know what happens when this is taken to the extreme.