Designing technical systems to be resistant to bias and discrimination represents vital new terrain for researchers, policymakers, and the anti-discrimination project more broadly. We consider bias and discrimination in the context of popular online dating and hookup platforms in the United States, which we call intimate platforms. Drawing on work in social-justice-oriented and Queer HCI, we review design features of popular intimate platforms and their potential role in exacerbating or mitigating interpersonal bias. We argue that focusing on platform design can reveal opportunities to reshape troubling patterns of intimate contact without overriding users' decisional autonomy. We identify and address the difficult ethical questions that nevertheless come along with such intervention, while urging the social computing community to engage more deeply with issues of bias, discrimination, and exclusion in the study and design of intimate platforms.