Choosing softer cuts of meat is healthy, but the fat on the meat is not harmful per se. However, if you want to avoid meat fat specifically, just eat healthier sources of fat:
avocado,
olive oil,
salmon,
nuts and seeds.
Ultimately, whether or not you should eat less fat depends on your preferred diet.
The truth is that meat can be a good source of nutrients. But the steak, chicken breast, or pork chop you choose for dinner is more than just “meat.” Carefully study food labels, choose the right sections, fat content, and more. You must know how to behave properly in the grocery store when choosing food.
