I must assume you noticed the brown streaks on the clothing as you pull them out of the washer and not when you pull them out of the dryer. The dryer too can cause brown streaks if the drum rollers or drum seals are worn out or missing.
If you know the brown streaks are definitely coming from the washer then the likely cause is one of two things:
Gunk breaking loose from the inner wall of the outer tub
I recommend removing the cabinet and tub cover ring and inspecting and cleaning the inner wall of the outer tub. Over a period of time and using cold water washes body oil, dirt and undissolved detergents will accumulate at the water line on the inner wall of the outer tub. After the gunk builds up thick enough parts of it will break loose at times when using hot water and then get on the clothes. I recommend inspecting and cleaning the scum by manually scrubbing and scraping it off if you find it accumulating. If you find no gunk on the inner wall of the outer tub the likely cause is transmission oil seeping up the agitate shaft or spin tube and getting on you clothes. The transmission would have to be replaced.
To access and remove the tub ring cover will require removing the washer cabinet. In order to remove the cabinet the console must be put into the service position to access the two cabinet retainer clips and to disconnect the lid switch harness connector.
First, disconnect the power cord from the power source
The console (key#26) will need to be placed in the service position by removing two (2) hidden screws, one (1) screw located at the bottom of the left hand end cap (key#7) and one (1) screw located at the bottom of the right hand end cap (key#10).
In order to access the two (2) screws hidden under the left hand end cap trim (key#8) and under the right hand end cap trim (key#15)the two (2) end cap trim pieces will need to be removed.
To remove the trim (key#8&15), place you finger behind the trim at the very top and bend it up enough to clear the console and then hinge it towards the front and off.
Remove the hidden screw under each end cap trim. Slide the console forwards about 1/4 inch and the raise it upwards and hinge it over the rear panel.
Disconnect the 3 wire lid switch harness plug located on the top. Pop the two (2) gold colored cabinet clips off.
Place the tip of a flat tipped screw driver down into the first valley and then push the handle end to the rear of the washer to pop off the cabinet clips. (See image below)
Open the lid and grab the opening and tilt the top of the washer cabinet forwards just a few degrees and then walk it backwards and off. (See image below)
Remove the tub cover ring by pulling the tub cover locking tabs outwards to unlock and remove the tub cover ring.
Look between the inner basket and the outer tub and you will likely find the accumulation of gunk.
Reverse the procedure to re-assemble the washer.