Is there a specific term that can be used for the people who do not drink tea or coffee like there is vegetarian in case of meat?
The short answer to your question is no, there is no specific term for people who do not drink tea or coffee. The general term for someone who avoids something is abstainer.
- a person who abstains from something regarded as improper or unhealthy, especially the drinking of alcoholic beverages.
- a person who abstains from anything.
abstain, verb (used without object).
- to hold oneself back voluntarily, especially from something regarded as improper or unhealthy (usually followed by from)
There is a word you can use, but it is not an established word:
This is based on the same-sounding word
which is someone who abstains from alcohol (link to Oxford dictionary online).
As commented by some users, there is no established word or term for someone who doesn't drink tea or coffee.
People who avoid consuming carbohydrates are called "carb-shunner" and you can consider using a tea-shunner and coffee-shunner.
The word shunner means
someone who avoids or keeps away from someone or something.
Or non-drinker of coffee (tea) could be used.