Rapeseed meal is a by-product of the oil-producing industry with a currently underestimated application. Two protein isolates, PI2.5–8.5 or PI10.5–2.5, were obtained from industrial rapeseed meal after treatment with an aqueous ethanol solution. The alkaline-extracted proteins were sequentially precipitated by two different modes, from pH 10.5 to 2.5, and vice versa, from 2.5 to 8.5, with a step of 1 pH unit. The preparation approach influenced both the functional and antioxidant properties of the isolates. The PI10.5–2.5 exhibited higher water and oil absorption capacities than PI2.5–8.5, reaching 2.68 g H2O/g sample and 2.36 g oil/g sample, respectively. The emulsion stability of the PI2.5–8.5, evaluated after heating at 80 °C, was either 100% or close to 100% for all pH values studied (from 2 to 10), except for pH 6 where it reached 93.87%. For the PI10.5–2.5, decreases in the emulsion stability were observed at pH 8 (85.71%) and pH 10 (53.15%). In the entire concentration range, the PI10.5–2.5 exhibited a higher scavenging ability on 2,2-diphenyl-1-picryl hydrazyl (DPPH) and hydroxyl radicals than PI2.5–8.5 as evaluated by DPPH and 2-deoxyribose assays, respectively. At the highest concentration studied, 1.0%, the neutralization of DPPH radicals by PI10.5–2 reached half of that exhibited by synthetic antioxidant butylhydroxytoluene (82.65%). At the same concentration, the inhibition of hydroxyl radicals by PI10.5–2 (71.25%) was close to that achieved by mannitol (75.62%), which was used as a positive control. Established antioxidant capacities add value to the protein isolates that can thus be used as both emulsifiers and antioxidants.