Question
Which varna are ‘Hindu’ Buddhists part of?
Answer
Since the Buddhists don't follow the Hindu Caste system they will fall in the category of "those having no cast"(or outcast) from the Hindu perspective.
If some generations ago some of their forefathers adhered to the Hindu caste system even then ,since that is all broken now,all the present Buddhists will fall in the outcast category only.Because mixed casts are outcast only.And,because there is no 5th caste in Hinduism.
Manu Smriti 10.4 Brahmano Kshatriyo Vaisyas Trayo Varna DvijatayoH|| Chaturtha Ekajatis Tu Sudro Na-asti Tu Panchamaha ||
Brahmana, the Kshatriya, and the Vaisya castes (varna) are the twice-born ones, but the fourth, the Sudra, has one birth only; there is no fifth (caste)
Now if you are among the ones who believe in a guna/karma-based caste system ,where one's birth plays no role,then i can't answer your question for sure.Because, then your guess is as good as mine.
But in Hinduism one's caste is mostly determined by birth,although gunas and karmas also play some role in it.
For example see the following verse from Manu:
Manu Smriti 10.3. On account of his pre-eminence, on account of the superiority of his origin, on account of his observance of (particular) restrictive rules, and on account of his particular sanctification the Brahmana is the lord of (all) castes (varna).
Here origin refers to birth,observance of some restrictions refers to karma and the sanctification process refers to the Saamskaras we have(viz-the 40 Samskaras,including Upanayana).
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