Should I move out during a whole home renovation?

For a full gut, yes. There is a point where the house has no working kitchen, limited heating and dust in every room, and staying through it costs more in stress than a short-term rental costs in money. For a phased renovation where work moves room by room, most households stay, with a sealed-off work zone and one functioning bathroom held back until the end. Decide this at the scoping stage, because it changes how the work is sequenced.