What about "red budgerigars" ?

A red budgie, the dream of every budgie breeder

The answer is very clear:

If you try to breed red budgies, you will go mad. The picture above is a fake, it is not possible to produce a red budgerigar.

I've read that some breeders who tried this occasionally got a single red feather, or a budgie that looks a little pink (mostly due to being on certain products like pink coloured mineral blocks) . But it's simply not possible to get red out of a colour chart like this:

Budgerigar Colour and Markings Chart (Image from the Budgerigar Council of Tasmania)

These birds are red and some of them look like budgies, but they're not:

Left: Rubino Rosella
Middle: Bourke Parakeet
Right: Red Canary

A word of advice: it's best to just let budgies choose whoever they want and let nature go its own way. Don't paint them or try other dangerous things in order to get a red budgie, because it's not possible and you're just going to make your budgie unhappy and sick.