While Nintendo hasn’t officially announced the option, it was revealed that stage hazards in Super Smash Bros. Ultimate can be toggled on or off. This was confirmed by Invitational players that have gotten up close and personal with Ultimate.
In the video, you can hear an Invitational player confirm that the option does exist, and he goes on to explain that one of the matches of the Invitational was played on Frigate Orpheon without stage hazards.
Please note: The video contains some explicit language.