Ram is as relevant to Muslims as it is to Hindus.
The events in the overall world during last 20 years or so, have made the entire planet extremely polarised, and India is no exception. There is general suspicion of people from other religion.
Granted, that Muslims would not worship Ram as a God. But can they deny the fact that Ram was few thousand years before Prophet Mohammad i.e. much before Islam religion came into existence. So why can't, at least Indian Muslims, revere Ram as a noble king who established an ideal kingdom, Ram Rajya, and feel proud about this king of our land?
When, Pakistani Abdus Salam, won the Noble Prize for Physics in 1979, I had felt extremely proud that a scientist from this part of the world had broken the hegemony of Europian scientists in the field of science.
Today fanatic religious leaders want Hindus to believe that Muslims have never acknowledged the existence of Ram.
Give me a break!!
There is an iconic song in the 1964 film Haqeeqat - कर चले हम फिदा जान-ओ-तन साथीयों which was penned by famous lyricist Kaifi Azmi. One of the verse of the song is as under:
खींच दो अपने खून से जमीं पर लकीर,
इस तरफ आने पाये न रावण कोई,
तोड दो हाथ अगर हाथ उठने लगे,
छूने पाये न सीता का दामन कोई,
राम भी तुम तुम्हीं लक्ष्मण साथीयों,
अब तुम्हारे हवाले वतन साथीयों
Incidentally, this song was sung by Mohd Rafi.
I also remember a story about Dr. Rahi Masoom Raza who wrote the screenplay & dialogues for the epic serial, Mahabharat. Once a lady reporter asked him how he could manage that being a Muslim. He suddenly became very silent appeared little upset. When probed further, he said "मै disturb इसलिये हुआ.. के तुमने यह कैसे मान लिया.. की रामायण और महाभारत.. मेरी विरासत नहीं है?
There would be many more such snippets of our History & Culture.