I better acknowledge my personal bias here: I'm a Muslim. Thus, of course I believe it is ideal that Eid can be more predominantly recognised as a religious holiday in Australia
Having said that, I don't believe that a public holiday for it is necessary at present. But I do believe it should be applicable for people to have like up to 4 religious days off work each year or something, for whichever religion a person practises.
I think that would be an effective way to acknowledge the multicultural policy which is meant to pervade in Australia (even if there is some dissension in this forum from this and support for assimilation instead).
It seems to me the point we are arguing or discussing is not Islam specifically, but religious/cultural tolerance. I believe that partly what makes Australia so great is its capacity (at least in theory) to recognise and appreciate the diversity of religious and cultural groups. By enabling religious holidays from work without having to pull a sickie or provide any other reason than the significance of a religous day, seems important to me to recognise said diversity.
I don't think it's appropriate to just deem the desire for recognised religious holidays of minority groups as a matter of come to our country, adopt our values. I was personally born and raised in Australia, so I don't consider myself a migrant (even if that technically makes me second generation migrant), and we are technically a secular society. Even if Christianity would be the dominant religion at present, different religious groups are growing at different rates and of course there are atheists out there so I don't think religious assimilation is something that fits multicultural or even human rights ideals.
Plus as some have mentioned if we want to get technical the Christian religion in Australia can be deemed a migrant religion since Indigenous religious beliefs existed for tens of thousands of years prior. That is in no way to disrespect Christians/ Christianity, but just to reaffirm that if religious priorities are to be based on migrant or naturalised status, then Anglo Saxons are also migrants
The majority is not always right. E.g. Indigenous peoples were classified under the Flora and Fauna Act in Australian until the 1967 Referendum, and I sure as hell don't think that the fact that it was commonly accepted made it right. As values of society change, so should our responses towards it in order to allow for true equality.
So yeah, I reckon that Muslim holidays should be recognised, at least to the extent that it is considered a valid reason for taking a few days a year off work. But that should be offered to every religious minority for major holidays as part of their personal, spiritual and religious beliefs.