Most Protestants (excluding a majority of Lutherans and Anglicans), don't cross themselves. What is the basis behind this?
Given the reformers emphasis on sola scriptura, this particular practice is not found in Scripture and was seen as idolatry by some reformers. Because Protestantism is rooted in the reformation, there is a historically rooted hesitancy to explore practices not found directly in the Scriptures. However, as with other traditions from throughout Christian history, there are Protestants today who are exploring the adoption of the sign of the cross (see second article). Certainly most Protestants would not feel that the sign of the cross had any special power, but perhaps they would adopt it as a reminder of what Christ has done for us.
It’s like why some Christians don't practice the laying on of hands when praying for others in a personalized manner. It’s why some Christians don’t hug when greeting people, when COVID is not a threat. It’s why some people don’t like to say “amen” out loud in appreciation of a sermon. It’s why some churches discourage clapping after a beautiful song. It’s why some like to lift up their hands to worship God while others prefer to fold their hands. It’s mostly due to cultural differences.