The vim way is to simply escape out of insert mode, do your movement commands, then go back in.
But you can also use ctrl+o [movement command] while in insert mode to do one-off movements and end up back in insert afterwards.
I honestly don't think however that you betray any vim sacred cows by using the arrow keys, or even the mouse when they are convenient. Such as when in insert mode.
hjkl is just much more convenient in normal mode while your hands are already in the right position.
But you can also use ctrl+o [movement command] while in insert mode to do one-off movements and end up back in insert afterwards.
I honestly don't think however that you betray any vim sacred cows by using the arrow keys, or even the mouse when they are convenient. Such as when in insert mode.
hjkl is just much more convenient in normal mode while your hands are already in the right position.