The Renewable Energy Directive (RED II) by the European Union (EU) provides an updated framework for the use of renewable energy in the EU transport sector until 2030, and bans the use of biofuels with a high risk of causing indirect land-use change in high carbon stock areas (high ILUC-risk criteria). The only biofuel feedstock affected by this criterion is palm oil. We employ the computable general equilibrium (CGE) model DART-BIO for a scenario-based policy analysis and evaluate a phase-out of palm oil-based biodiesel, and an additional phase-out of soy oil-based biodiesel in the EU. Our results show that the palm phase-out has only a relatively small impact on global palm fruit production and total crop land use in tropical and subtropical regions, while the soy phase-out leads to a comparable stronger decrease in global soy production, and a reduction in total cropland use in soy-producing regions. Both policies lead to increased oilseed production in the EU. Therefore, farmer in Malaysia and Indonesia face a significantly reduced income. While European farmers profit the most, EU firms and households are confronted with higher expenditures. Finally, this study indicates that unilateral demand-side regulations for a single good in a single sector is not sufficient for effective environmental protection. Enhanced binding sustainability criteria and certification schemes for the use of all vegetable oils in every sector and industry as well as improved protection schemes for sensible forest areas are necessary.