Farmers Conserving Agricultural Resources through EQIP Act or the Farmers CARE Act This bill reauthorizes and modifies the Department of Agriculture (USDA) Environmental Quality Incentives Program (EQIP). (EQIP provides financial and technical assistance for agricultural producers and land owners to implement certain conservation practices.) The bill expands and modifies the purposes of the program. It also includes modifications that: increase payments for certain land management and vegetative practices that result in highly cost-effective treatment of priority resource concerns; prohibit payments for large confined animal feeding operations to construct an animal waste management facility or any associated waste transport or transfer device; repeal the allocation of funding for practices relating to livestock production; increase the allocation of funding for practices relating to improving fish and wildlife habitat; specify an allocation of funding for producers who participate in an independent animal welfare certification program; add payments for certain practices that promote ground and surface water conservation; remove the payment limitation for practices related to organic production; add payments for certain conservation practices related to antibiotic use and pasture-based production systems; prioritize applications that address priority resource concerns identified by USDA; and reduce the limitation on total EQIP payments.