Exactly. The term we use to categorize Italians is "Italian".

https://www.ethnicity-facts-figures.service.gov.uk/style-guide/ethnic-groups/#2021-census

In Britain it's used in most forms that check for diversity etc.

updated text and information :

https://lemmy.world/comment/13904300

So, the idea is more in the way race is actually percieved, and how unjust it is, and in the people who are usually regarded outside the "desirable" label try to fit into it, while only recieving partial recognition.

"European" is usually used to indicate positive aspects, and people from greater europe usually enjoy claiming that origin to label themselves with the positive aspects that come with it.

Although when you look at attitudes in europe, it's more fragmented and nuanced, with many additional barriers and classifications. For example, PIIGS :

https://en.wikipedia.org/wiki/PIGS_(economics)

Portugal, Italy, Greece, and Spain (And Ireland) are accepted as european, but with the idea that they are not as deserving of the criteria due to economic troubles. This marks a cultural two tier european perception within europe, with places like Germany looking down on Spain or Italy. Astute readers may mark that all these countries (except ireland) are mediterranian, and racism against the Irish has its own history.

This also happens to eastern europe :

https://en.wikipedia.org/wiki/2004_enlargement_of_the_European_Union

https://en.wikipedia.org/wiki/2007_enlargement_of_the_European_Union

Each wave coming with it's own conservative scaremongering of immigration (despite a lot of needed professionals of high quality and work ethic migrating from said countries) and racist BS. Thus, someone from Poland or Romania are seen as "european" but with a large asterisk.

When those people try to claim the "white" or "european" indicator to take advantage of the positive perception, it feels like they are trying to claim to be something that they are partially gatekept outside of.

Of course, there are noble aspects to people and zones all over the world. This is all silly and irritating and basically racist.

However, I personally find it stupid when people who are about to be marginalised try to claim in group status by the in group that doesn't 100% support them. They are trying to fit into the in group to further their own agenda, instead of advocating for a non in-group/out-group status.

Hence, the joke that Mediterranian countries like italy or morocco. Because the kinds of itallians that are trying to bust their ass to seem "white" would take offence to being painted with the same brush as "africans". They quickly forget that the Roman empire spread all over the middle east and north africa, and those parts currently seen as "undesirable" were a valid part of the empire.