Here at Brazil, ethanol is produced from sugarcane. And sugarcane farming is actually illegal in the Amazon. The President tried to make it legal, but fortunately his decree was suspended by the Judiciary [1].
I don't doubt there may exist a few illegal sugarcane farms in the Amazon, but given how huge sugarcane farming is in southeastern Brazil, I don't think any Amazon sugarcane would significantly contribute to Brazilian ethanol production.
> Soy culture is used to create a cheap protein feedstock for the meat industry.
Soy is more of an issue for Amazon than sugarcane. But, just as you said, it is used to feed cattle, and the main issue resides in the cattle. Cattleman in Amazon usually adopt the extensive breeding system, so lots of area are required to breed cattle.
[1] https://www.conjur.com.br/2020-abr-21/juiza-suspende-decreto...
Most likely, you eat U.S.-raised beef and burn gasoline from oil that comes from the U.S. or Middle East. Surely you are adding to the global warming, but it has nothing to do with Amazonian forest being illegally cut.
In Brazil, most if not all cars run on ethanol [1]. The U.S. produce massive amounts of ethanol domestically [2] so, most likely, whatever gasoline you might be buying in the US, it's not using Brazilian ethanol, even though the U.S. does import some Brazilian ethanol [4], it's dwarfed by the domestic production [2].
U.S. beef is raised so efficiently that farmers manage to export it to Mexico an China, among other places [3], while receiving virtually no subsidies. You likely need to specifically look for gourmet Brazilian beef if you want to have a chance to taste a cow illegally raised on a pasture which used to be Amazonian forest.
[1]: https://en.wikipedia.org/wiki/Ethanol_fuel_in_Brazil
[2]: https://en.wikipedia.org/wiki/Ethanol_fuel_in_the_United_Sta...
[3]: https://www.fas.usda.gov/beef-2020-export-highlights
[4]: https://www.eia.gov/dnav/pet/pet_move_impcus_a2_nus_epooxe_i...
https://www.statista.com/chart/19122/biggest-exporters-of-be...
Also US-raised beef also occupies the area of destroyed forests. American beef didn't destroy the Amazon but it destroyed the environment anyway and is every bit as guilty of producing global warming.
Blends of E10 or less are used in more than 20 countries around the world, led by the United States, where ethanol represented 10% of the U.S. gasoline fuel supply in 2011.[1] Blends from E20 to E25 have been used in Brazil since the late 1970s. E85 is commonly used in the U.S. and Europe for flexible-fuel vehicles. Hydrous ethanol or E100 is used in Brazilian neat ethanol vehicles and flex-fuel light vehicles and hydrous E15 called hE15 for modern petrol cars in the Netherlands.[2]
https://en.m.wikipedia.org/wiki/Common_ethanol_fuel_mixtures
If you live in the US and drive a car or eat meat, you are likely to be co-responsible.
Soy culture is used to create a cheap protein feedstock for the meat industry.
Modern car fuel contains ethanol (10% in the EU). The ethanol is produced by having micro organisms convert biomass. The idea being that you use the short carbon cycle (already in the eco system) instead of the long carbon cycle (stuff that has been in the earth for 200My) thus effectively reducing carbon emissions.
Both of these are produced in Brasil, both have a footprint much larger than the gold or exotic wood markets (which are tiny, compared with meat and car fuel)