[LouieFisk]

“During the reign of Constantine’s sons, paganism continued to be practiced throughout the empire.”
—
Since Constantine went back forth between Christ and Sol Invictus (the invincible sun god) as he deemed needed to run the Empire and military, the kids were just following the old man’s example.

[Antoninus]

Since Constantine went back forth between Christ and Sol Invictus

There is no evidence that Constantine "went back and forth". After AD 312, it was a straight line from Sol Invictis to Christ. After ca. AD 324, there was zero doubt in anyone's mind that Constantine was a follower of Christ, if still a catechumen at that point.

Keep in mind that the Roman Empire was (it's estimated) about 85% pagan when Constantine converted, and it did not change instantaneously after his conversion. Even during the reign of Justinian some 200 years later, there were still large pockets of paganism throughout the empire.