Williams, a devout Muslim, appeared for the Blues during Saturday's loss to the Otago Highlanders with the Bank of New Zealand (BNZ) logo on his collar blocked out by tape.
His action took New Zealand Rugby (NZR) and the Blues by surprise, prompting discussions this week with Williams and his management.
NZR said it was accommodating Williams' "conscientious objection" by allowing him to wear a Blues jersey with no branding from BNZ or Investec, Super Rugby's main sponsor.
"Williams has now clarified his preference is not to wear logos from banks, alcohol brands and gambling sponsors on his team uniform," it said in a statement.
Williams' logo cover up was prompted by Islam's objection to usury – earning high interest from loans.
NZR said Williams had no concerns about AIG, the All Blacks' shirt sponsor, because it is an insurance company.
However, the US giant's latest financial accounts show it has a commercial mortgage portfolio of US$25 billion, upon which it levies market interest rates in the same manner as BNZ or Investec.
Williams said his stance was "nothing personal" against the finance firms, but reflected a wish to feel comfortable as he developed a deeper understanding of his religion.
"So while a logo on a jersey might seem like a small thing to some people, it is important to me that I do the right thing with regards to my faith and hope that people respect that," he said.
New Zealand Prime Minister Bill English questioned Williams' behaviour this week, saying he did not understand why one player should be treated differently to his teammates.
However, NZR general manager of rugby Neil Sorensen said it was an issue of faith.
"Sonny holds clear religious beliefs in relation to this matter and we respect those," he said.
"Conscientious objections need to be genuine, and we believe this is."