They haven't actually been asked to build it so the "refuses" in the title could cause confusion. "would refuse" or "say they would refuse" would be clearer and

They haven't actually been asked to build it so the "refuses" in the title could cause confusion. "would refuse" or "say they would refuse" would be clearer and best would be just using the article title "Of 8 Tech Companies, Only Twitter Says it Would Refuse to Help Build Muslim Registry For Trump"