Hastings has been outspoken on several hot-button issues being targeted by the new administration, including immigration and net neutrality.
"You want the CEO that is going to do what's right for his company and his shareholders," Cuban said.
Donald Trump's administration has instituted a travel ban on immigrants from seven Muslim-majority countries — Iran, Iraq, Syria, Libya, Somalia, Sudan and Yemen — and temporarily halted the entry of refugees.
"Trump's actions are hurting Netflix employees around the world, and are so un-American it pains us all," Hastings said on Facebook.
Cuban said he would prefer for companies that he invested in to be outspoken about the policy. For instance, any company hoping to hire an talented engineer working on artificial intelligence now has to consider the logistical challenges of their immigration and travel plans, Cuban said.
"That type of uncertainty is not good for anybody," Cuban said.
Trump's FCC pick, Ajit Pai, has told CNBC that he opposes net neutrality policies that reclassify broadband as a public utility.
In the company's most recent earnings, Netflix said, "we hope the new U.S. administration and Congress will recognize that keeping the network neutral drives job growth and innovation."
Cuban — who as founder of dotcom-era company Broadcast.com, is not stranger to online content creation — said he's long been against net neutrality.
Disclosure: CNBC owns the exclusive off-network cable rights to "Shark Tank," which features Mark Cuban as a judge.