So here’s an optimal compromise that will both ensure some grip training, ensure that your training doesn’t suffer and maybe make everybody happy. Assuming grip is important, start pulling workouts without straps. Depending on how good your grip is you’ll eventually find grip starting to become limiting. It might be on your fourth sets of deadlifts, your third set of rows, whatever. Doesn’t matter when it starts to happen. Just that it does at some point.
At this point, strap up. Your grip has been trained but this will prevent you from limiting your actual workout by a failing group. Then, if you want to improve your grip, do some actual grip training. I know, crazy idea but if something is limiting, train it a bit extra at the end of the workout if it’s important to you. You get grip work during the initial stuff, don’t let grip limit the other training AND work to fix a weak point.