the reason behind the importance of the site isnt because it was built on some random hindu temple, its the alleged birthplace of a character central to the hindu mythology. theres nothing special about the site of this temple other than the aforementioned claim that its the birthplace of rama, hence its importance is grounded solely in mythology. you admit as much in the last sentence of the first paragraph.
+100 points in unintended irony when u claim Muslims have a world view of once a mosque always a mosque, when u wanna rebuild a temple which may have existed more than 500 years ago.
my take is that if there was a temple and it was destroyed go complain to the people who did it, if they are dead, move on. theres hundreds of mosques which were catherdrals, tonnes of cathedrals built on historic mosques, or native American temples, theres mosques and churches built on sites of historic jewish importance. it is what it is, if you go down the road of mythological deeds of ownership you just end destroying tonnes of architecture, history and culture. if you are really desperate, just co-opt a building, like the hagia sophia or like the cathedral of cordoba.
im glad as i suggested you didn't hide ur contempt for the other side, your open in your views and i appreciate that, and it makes your whole view point understandable.