Yes, the USA should continue to allow trade with China despite ongoing media crackdown, because these two economies are very much connected and any disruption in trade would hurt both countries financially. Business doesn't care much about freedom of speech or human rights. After all, the USA is still buying oil from Saudi Arabia despite constant reports of human rights violations.
The United States should always trade with China. Yes, China is often guilty of human rights violations, and crackdowns on civil liberties. However, cutting off trade and economic ties with China would not solve any of these problems. Instead, it would only alienate the Chinese government; potentially raising the stakes of a war between American and China. Trade between nations will always increase cooperation and make both countries more wealthy. This provides an incentive for countries not to go to war with each other.
China is a country packed with factories. All that is seen there is the industrial development of new products, dirty and clean alike. Many many products are imported from China. Not just to the United States, but also to many other developed countries. In the case of the U.S, trade with China should continue to be open, but with some regulations.
News is not a human right although unfortunately it does reveal the truths of human rights violations in a country where it is ever so rampant. The Chinese government cracked down on the media but the United States is not about to let that stop them from doing trade with them simply because economics are more important to our country than almost anything else, despite what the government would like us to believe.