How does the Anglerfish being blind help me avoid them?

Because the anglerfish are blind, they cannot see you, but they can hear you, especially your suit and ship thrusters. This means that you need to go through Dark Bramble very quietly. Your suit and ship thrusters will alert them above very minimal thrust, but it can be tricky to regulate the exact thruster output allowed. The more consistent method is to not use thrust at all while a fish is in the room.

Gain as much speed as possible before entering the anglerfish room and then cut off all input (I usually set my controller on the table while floating by just in case). Wait until you are well past them before making any other jetpack inputs. You maintain momentum pretty well in space, so you should be able to make it to the other side of the room with only an initial boost at the beginning.

This video demonstrates the technique in action: