Step 1: Understand what is being asked.
We need to pick the person whose set of preferred festivals contains both Holi and Eid, and at the same time does not contain Diwali or Christmas.
Step 2: Go through each person's list.
A: Holi, Dussehra, Diwali, Guru Nanak Birthday - has Holi but also has Diwali, so A is ruled out.
B: Shivratri, Christmas, Onam, Eid - has Eid but also has Christmas, and has no Holi, so B is ruled out.
C: Holi, Shivratri, Christmas, Diwali - has Holi but also has Christmas and Diwali, and has no Eid, so C is ruled out.
D: Holi, Dussehra, Guru Nanak Birthday, Eid - has Holi and Eid, and does not have Diwali or Christmas, so D satisfies every condition.
E: Christmas, Diwali, Onam, Guru Nanak Birthday - has neither Holi nor Eid, so E is ruled out.
Step 3: Match the person to the option.
Only D fits the condition of enjoying Holi and Eid while not enjoying Diwali and Christmas. Among the four choices listed for this question, D is the third one.
Final Answer:
D is the person who enjoys Holi and Eid but not Diwali and Christmas. \[ \boxed{\text{D}} \]