Namecheap is the default mainstream domain registrar that most adult operators use without issue. The registration side has no content policy — you register the domain, you point it where you want, Namecheap does not police what the site serves. Their related services (shared hosting, email, SSL) have stricter content policies; ignore those and use Namecheap purely as a registrar.
Pricing. Competitive across the industry — .com renewals are in the $10–$13/year range, transfer pricing comparable. WHOIS privacy is free and on by default (matters more than people realize — you do not want your home address in the WHOIS record for an adult site).
What to actually use. Register, set DNS, point at your adult-friendly hosting. Do not use Namecheap's shared hosting or email forwarding for an adult business — their AUP on hosting prohibits adult content and enforcement is real. Use a registrar for what registrars do, use specialists for everything else.
Domain considerations for adult sites. Some TLDs are friendlier than others — .com is universally accepted; .xxx exists as an adult-specific TLD but has tradeoffs (some search engines, ad platforms, and payment processors treat it differently); .tv and .cam are common alternatives. Avoid country-code TLDs whose registries have restrictive content policies (the .us policy is restrictive; .co is permissive).
Bottom line. Default registrar choice. Compare against NameSilo for renewal-cost optimization and Dynadot for marketplace access.