I'm Algerian. You can ask a million Algerians and get a million different answers.

Just understand that there is a large segment of Amazigh people who do not speak Arabic, do not identify as Arab, and have rarely interacted with Arabs. This makes them naturally combative (hence the Joe Budden meme) when other Algerians or foreigners label them as Arab. Some individuals will also find it doubly offensive considering the fact the Algerian state has tried to homogenize the country by forcing them to speak Arabic - so being called an Arab would be the equivalent of being identified as your own oppressors. Imagine an African American being identified as white for instance (although the oppression doesn't match that of slavery or Jim Crow). People who strongly identify as Amazigh and proud will be seen sporting these cool flags.

In Algeria, you'll find people who fall under all walks of life. The region was colonized or invaded by several groups of people over history (Romans, Phoenicians, Turks, Arabs, French). There are strong traces of Christianity (St. Augustine), Judaism, Islam, and polytheism found from the past 1000 years. You'll naturally encounter people who hold many identities in the diverse cities. Some Algerians claim Turkish origins by name. There are also Algerians that trace their roots entirely to Arab traders from Yemen. And there are ones who are completely Berber/Amazigh but still identify as Arab because they were Arabized and grew up speaking Arabic. It's weird.