I don't believe Qantas has a special meal selection that is "No red meat and no cheese". They have vegetarian, although many airlines are now combining Vegetarian meal with Vegan meal since the Vegan meal also meets the Vegetarian requirements - well maybe in content, but not in flavour

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The only way to ensure no cheese would be to order non-dairy, which will eliminate the "yummy deserts".
On international flights in economy, there is generally a choice of two hot meals. I have never seen a case where noth choices are red meat. At least one is usually chicken or fish.
And in most cases, the cheese content is a wrapped block of cheese to go with the dry crackers. It is your choice to eat of leave it wrapped. However, there may be cases where some cheese product is used in the sauce of the main dish. So if you are alergic to cheese then that may not be an acceptable risk.
There seems to be a trend in airlines to reduce the range of special meals offered. They cost the airline money and many people have been ordering them just because they think they may get a better quality meal than the standard meals offered. They were originally provided to meet the medical or religious dietry requirements of some passengers. But given the number of times I have seen situations where requested special meals have not been loaded, I recommend that if you have special medical or religious dietry needs, that you BYO food for the journey - it will be safer.
If you just prefer not to eat red meat or cheese, then I suggest you may be better off just requesting the chicken or fish dish when the trolley comes past, which will ensure you get the yummy desert. If there is amedical or religious reason for avoiding these food types, then learn to like Vegan meals because that is what you are likely to receive.
Of course you can always pay to fly business class and enjoy a widr variety and enhanced menu quality ... and even ymuuier deserts. You can always decline the after dinner cheese selection and just ask for two Baileys instead - I've never been declined multiple Baileys for desert in QF business class :wink: .
PS. Man didn't make it to the top of the food chain to become a vegetarian

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