Mechanical pump is a diaphragm and some check valves. The check valves are ball bearings that open when the diaphragm is pushed away from the check valve. So it "sucks" fuel from the tank and "pushes" fuel to the carb. Any dirt will stop the check valve from seating. That would let fuel get "pushed" back to the tank, and "sucked" from the carb. Not the way you want it to work. A filter inline from the tank to the pump is just insurance that the pump will work as it was intended. Won't hurt anything. And it could help. Electric pumps have an impeller to push fuel to the engine. Dirt will destroy that in short order. So a filter between the tank and pump is standard. I like a clear filter that I can see the dirt in. Lets me know when it needs to be changed. A filter inline from the pump to the carb is to protect the carb. Again, I like a clear filter that lets me see what is in there. And yes, I run both. The filter won't care if fuel is pushed through it or sucked through it. Only issue would be if it leaks. Most of the movement is very low pressure hydraulic any way. If you take the fuel line off the pump with a full tank of gas it will run out like crazy if you don't cap the line.
