We examine the implications of privacy-motivated targeting restrictions on consumer welfare, advertisers' customer acquisition costs, and platform revenue. In our model, competitive product firms reach consumers by placing informative ads on a monopoly advertising platform; consumers are horizontally differentiated in their product preferences and in their willingness to pay for a less preferred product, but they don't have any intrinsic privacy preferences or an aversion to mistargeted ads per se. In this context we show that both the platform and consumers would be better off without privacy restrictions if ad rates are exogenous to the privacy regime. However, in the more realistic scenario of endogenous ad rates, consumers with flexible product preferences are likely to be better off under privacy. This is because a platform with market power recognizes the threat cross-selling by mistargeted ads poses to ad volume and compensates by lowering ad rates. Flexible consumers benefit when competitive product firms pass on their advertising cost savings in the form of lower product prices.