QUESTION:  What is the position of greeting a fellow Muslim with salam? And is it wajib upon everyone to return the Salam despite whatever circumstance of that particular person is in? 

Answer: Greeting with salam to one another is sunnah, however, it is wajib to return the salam based on the Qur’anic verse where Allah says: “And when you are greeted with a greeting, greet with a better (greeting) than it or return it; Surely Allah takes account of all things”.[1] [Surah An-Nisa:86]

And in the hadith: Narrated by Abu Huraira r.a “The prophet s.a.w. said you will not enter paradise until you believe, you not believe until you love each other, should I not inform you about a thing that when you do will love one another? Spread salam (peace) amongst you”. [2] [Sahih Muslim:86]

As for returning the salam, however there are some exception applies. Allamah Ibn Abidin Shami r.a one of the greatest and last Muhaqqiq (great researcher), great faqih of Hanafi Madhab in his famous Fatwa kitab Radd al Muhtar or known as Fatwa Shami (which is widely accepted and regarded as highest authority in the Hanafi Madhab) has mentioned by quoting from Jalal Uddin As-Suyuti r.a poetry work (who is a Shafi’e scholar) that it is not wajib to return the salam (for a person) on the following twenty one places:

1. [Salah] At the initial stage of Islam people used to make salam while in Salah including talking to one another. Later on this practice was abrogated. Similarly many people when entering Masjid makes salam while there may be many people engaged doing Salah or even wating for Jam’ah and doing Zikr thus, its makruh to do so. [3] {1} Sahih Bukhari:1200 {2} Sahih Muslim:539 {3} Sunan Abi Dawud:949 {4} Sunan Tirmidhi:405 {5} Sunan An-Nasai:1219 {6} Sharh Mayanil Athar vol-1:170 {5} Surah Baqarah:238  
2. [Eating]
3. [Drinking]
4. [Reciting Qur’an]
5. [Dua] When one is busy in making supplication
6. [Zikr] One is engaged in doing Zikr
7. [Khutbah] When Imam is delivering the khutbah
8. [Talbiyah] When one is engaged in Talbiyah during hajj
9. [Qada-e-hajat] On relieving oneself in toilet
10. [Iqamah]
11. [Azan]
12. [Given salam to a child] Who does not have understanding
13. [Drunk] A person who is in a drunken state should not be given nor returns it
14. [A young woman] When fear of fitnah to do salam or return salam
15. [Fasiq] Evil doer
16. [Drowsy] A person who is feeling drowsy or in slumber
17. [Sleeping]
18. [Sexual intercourse]
19. [During reconciliation]
20. [Bathroom] While bathing
21. [Insane]

These quotes are based on many authentic ahadith where the fuqaha (JURISTS) has deduced from and compiled it together for ease of references. 

Reference: [4] Fatwa Shami vol-2:386