I regularly see people discuss the possibility of domain registrar front running. In fact, I’ve written about this topic before. By and large, I can’t imagine any reputable domain registrars doing this today for many reasons.
Front-running accusations often stem from someone searching for a domain name at a registrar, seeing that it’s available, choosing not to register it, and later finding it has been registered when they check again. Whois privacy complicates this because the actual registrant may not be shown. In fact, with some Whois privacy services, it can look like the domain name is owned by the registrar itself. In addition, default registrar landing pages can also muddy the waters.