What is the opinion of Buddhism on the caste system and untouchability of Hinduism? The Varnashrama dharma (caste system) is the backbone of Brahminism (Hinduism), untouchability is a part of that social order. We all know that Gautama Buddha was against Varnashrama dharma, and rejected the Vedic religion. But unfortunately, we see caste system and untouchability in many 'Buddhist' countries. For example, the Burakumin/Eta in Japan, Baekjeong in Korea, Ragyabpa in Tibet, etc. As we know as Buddhists that the Buddha was no hindu, then why this system is also in the societies of Buddhist countries?
Actually, Gautama Buddha was not against the caste system in mainstream non-Buddhist Indian society however he did emphasize social status ('caste'/'jati') was dependent upon here-&amp;-now kamma rather than on physical &amp; social birth (refer to MN 93, MN 98 and other suttas in the Brāhmaṇa Vagga). For example, he often emphasized a Brahman priest or caste member that does not adhere to the five moral precepts is not a Brahmana or Holy Man. 

The Pali suttas have the following examples: 


It was declared the Buddha "does not seek any harm for the line of brahmins" (MN 95). 
The Buddha criticised Brahmans who marry &amp; have sex with non-Brahmans. (AN 5.191)
The Buddha said wives who are immoral are expelled or caste out from families (MN 37.30). 


The Pali suttas show no opposition to the non-Buddhist Indian caste distinctions however the Pali suttas do explicitly say when a person joined the Buddhist Community (Sangha) they automatically lost their former caste status or name (AN 8.19). 


  (4) “Just as, when the great rivers … reach the great ocean, they give up their former names and designations and are simply called the
  great ocean, so too, when members of the four social
  classes—khattiyas, brahmins, vessas and suddas—go forth from the
  household life into homelessness in the Dhamma and discipline
  proclaimed by the Tathāgata, they give up their former names and clans
  and are simply called ascetics following the Sakyan son. This is the
  fourth astounding and amazing quality that the bhikkhus see in this
  Dhamma and discipline….


As for contemporary Asian societies, many of these societies were previously or concurrently Hindu in relation to the arrival of Buddhism. Similar to when the Buddha was alive, Buddhist monks generally do not act to oppose &amp; destroy other religions. Buddhism is not like Judaism or Christianity. Thailand is an excellent example, where most religious people still follow other religions, such as spirit, ancestor or Brahma worship (even though they consider themselves "Buddhist").