First of all few people “live by caste”. It is salient for certain domains such as marriage, religious beliefs/rites, food and occupation and not much thought about for others. So how a Hindu might feel about outsiders* depends on how much they are impinging on those particular domains.

For example, in my community Mexican food is well regarded as it is spicy and there are good vegetarian options but Mexican religion (Catholic or Evangelical Christianity) has low status because it’s beliefs are alien and in some cases perceived as hostile. There is no general theory of Mexicans though. To the extent that Blacks and Hispanics are considered lower and Whites higher is because the host society mainly sees them that way. Where that has local variations, we too tend to follow suit. My relatives in Texas some of whom are conversant in Spanish have a higher regard for Mexicans than those in the Northeast because that is true for Texans and Northeasterners in general.

* Outsider also applies to Indians. I am a Gujarati Brahman and I feel some affinity to South Indian Brahmans because we share customs and food ways but say Bengali or North Indian Brahmans not so much. My community tends to be lukewarm to hostile to Muslims but Gujarati Muslims can in some contexts be “one of us” because of shared language. Brahmans traditionally do not socially mix with lower castes but I have some friends from such backgrounds because they like me are devotees of Shiva whereas “establishment” Hinduism in Gujarat is mainly Vaishnava.