This is a question I have about Hinduism. How does Hinduism believe they should treat those inside and outside of their cultural frame?
Hinduism basically asks for well-being for all people. And all people here means those who belong to the religion plus those who don't. So, treatment should be based on equality and not based on discrimination.
Have a look at the following verse from Upanishads:
ॐ सर्वे भवन्तु सुखिनः सर्वे सन्तु निरामयाः ।
सर्वे भद्राणि पश्यन्तु मा कश्चिद्दुःखभाग्भवेत् ।
ॐ शान्तिः शान्तिः शान्तिः ॥
Om Sarve Bhavantu Sukhinah Sarve Santu Nir-Aamayaah |
Sarve Bhadraanni Pashyantu Maa Kashcid-Duhkha-Bhaag-Bhavet |
Om Shaantih Shaantih Shaantih || ....
1: Om, May All become Happy,
2: May All be Free from Illness.
3: May All See what is Auspicious,
4: May no one Suffer.
5: Om Peace, Peace, Peace.
So "Sarva bhavantu sukhinAh" Or "Sarva jana sukhino bhavantu" or "May everyone be happy" is the very core idea of Hinduism.
In Vedas too, we find Mantra which says to speak the Mantras to even strangers. So, it is asking not to discriminate between own people and strangers.
YathA imAm vAcham kalyAnim AvadAni janebhyah (1)
BrahmarAjanyAbhyAm sudrAya cha AryAya cha (2)
SwAya cha aranAya cha (3)
May i speak the sacred word to the masses of the people (janebhya) (1) to the brahmana, kshatriya, to the sudra and the Arya (2) and to our own men and the strangers (3).
Shukla Yajur Veda 26.2
Concord among people, among different nations is also being spoken in the following Atharva Veda Mantra:
SamjyAnam nah svebhih (1)
SamjyAnamashivanA yuvamihAsmAsu ni yacchatam (3)
Let us have concord with our own people (1), and concord with people who are strangers to us (2); Asvins, create between us and the strangers a unity of hearts (3).
Atharva Veda 7.52.1