Never put meat or dairy in your composter.
We won’t put bread either - husband says it’s because it has fats which might go rancid. No dog poo. No clippings that have weed killer exposure. Leaves are terrific - but oak takes a longer time to break down. All kitchen scraps except ones mentioned above are fine. Egg shells, coffee and tea, greens, fruit and veg debris, yes. We toss in the remains of HEALTHY spent garden plants at end of season. We have a few hens so their manure sometimes goes in to enhance. Good, natural mulch, newspaper bits, and that sort of thing as long as it has no bad chemicals.
We don’t do twigs as they take too long to break down.
Consider starting a worm composter too.
Commercial bread might, but for every 750 gram loaf that I make, about 12 grams of oil get added, so I don't worry about it.
Problem I have with my bread is it goes bad in about 4 days because there are no preservatives. So in the compost it goes.
/johnny