There is no question at all that synthetic antibacterial substances, often added to consumer products, will directly breed resistant bacteria.
As one ubiquitous example, please research triclosan's effects on bacterial biology, as well as its environmental impact. Triclosan will degrade into dioxin and other carcinogens when exposed to sunlight. The proof is in the pudding.
Lastly, even if there were such a synthetic additive which somehow did not potentiate microbial resistance, it would still likely add to our constant daily bombardment of carcinogens.
Trading short term pathology for a longer term pathology, which costs hundreds of billions of dollars annually to deal with, is not a very wise public health strategy. There are no short cuts.