Who decides which stance a newspaper takes on Brexit, it's surprising that sister newspapers can take opposite views?

Usually the owners or board of directors decide. The owners or board of directors then inform the managing editor of their wishes.

Fox News was just bought by Disney enterprises, for example. Almost immediately afterward Judge Jeannine Pirro was fired.

At times the media play one side of politics against the other to keep their readership up.

Depends whether editor has full control. Some do to allow them to set the direction and tone. Others it is dictated by the owner(s).