Here we have another example where the subordinate conjunction that has a resultive meaning (‘with the result that’). Such usage is somewhat unexpected for speakers of modern English, so there has been a tendency in the history of the text to replace the that with and. Here in Ether 12:14, the change was made in the 1874 RLDS edition, but the 1908 RLDS edition restored the correct that. For a list of additional examples of the tendency to replace resultive that with and, see under 1 Nephi 11:29.
Summary: Maintain in Ether 12:14 the original resultive that in the clause “that they were baptized with fire and with the Holy Ghost”.