When you omit the rest breaks between sets, you alter the training effect of the workout. However: the single most important factor in the effectiveness of your workouts is doing them consistently. So if skipping the rest breaks makes it more likely you're going to do the workout in the first place, you're serving yourself well by doing so.
There are two other options to consider here though:
1. Fit December is designed to be a beginner friendly program the whole family can do together. So the specified rest breaks are long. Since I workout alone, I consider the rest protocol to be "up to 2 minutes" and take only what I need to get the maximum training benefit out of the workout for myself. This can differ depending on the specific exercises in the workout. (For example: for myself, I would only take 30 second breaks on the days with standing exercises. My conditioning level is such that I can do them flat out and still be almost 100% recovered after a 30 second break. For the floor work, however, I can work at a greater intensity if I take one minute breaks.)
2. "Break" doesn't need to mean "do nothing". You just need to rest the primary targets of the workout. Fit December Day 3 is an ab-focused workout. You'd still be taking a "rest break" if, for example, you stood up between sets, walked around, and did some chest expansions or overhead fist clench/unclenches until it was time to get back to the ab work. (I'd recommend keeping your "break" exercises light, unless you are comfortable with how to sequence safe and effective supersets.)