I have heard people debating whether Islam and Norouz are „compatible“.

Here are my thoughts:

First of all, Norouz is a national celebration of all Iranians independent of ethnicity, dialect or religious belief while Islam is one among several religions.
From a rational point of view there is no „either, or…“ to decide about.
You can be atheist, Zoroastrian, Muslim, Bahai..and celebrate Norouz.

In case of Islam, no matter whether you are a practising pious Muslim or a mainstream Musim there is no reason to not celebrate Norouz. This is because Norouz does not violate any islamic principles. It does not hinder anyone from believing in God, prophet Muhammad or the herafter.

Contrary to a wide spread but wrong understanding of piety Islam is not hostile to being happy or celebrating. Islam does not demand from a Muslim to do nothing else than praying or fasting or reading Quran.

Some calls for banning Norouz because it allegedly contradicts Islam are as absurd as banning TV programs or sports because these activities supposedly distract people from performing their „religious duties“.
This is of course complete nonsense. Norouz´ entire duration is 13 days and even during that period anyone can pray or fast or read Quran as much as he likes.

Religious zealots must be cautious not to alienate people against religion by unnecessary and out of perspective radicalism. They are doing a disservice to religion by placing and portraying it as an antipole to everything that people love.
Don´t blame religion. Blame (some) religious people.