The general rule to stop your general motion is to have a shutter speed at 1 / (focal length * crop factor), so in your case, if you are really good at holding still during the shot, the guideline for the 135L is 1/160th for FF.
If your subject material is also moving, assume they are not able to maintain a still moment like you, so perhaps 1/250th for subjects, not quite double.
This definitely points to 1/500th with the 135L on FF to be the guideline you want with live subjects. This is what I strive for, and only go lower once I have hit limits with aperture and ISO. This is especially the case when taking pictures of children.
When shooting sports, I know many try to shoot at 1/800th to 1/1250th, but after several years of sports shooting, I personally have settled on a shutter speed of 1/2000th. This is the speed one needs to stop water droplets in air as they fly off players. Each situation you shoot, you need to experiment to find the settings that give you the best baseline to start with. Each person with their respective gear for what they shoot will have different settings.