Your rifle does not care that the necks are dirty.
I tumble my brass in dirty walnut-shell media for about 4 hours. Most of my brass comes out looking like that. Been using the same RCBS sizing die since the 90's. So I can safely say dirty case-necks "don't hurt" the die. Probably sized a good 50,000 cases (that looked just like that) in that die. The gun doesn't care.
If you like squeaky-shiny brass, there are ways to turn the most disgusting, dug-out-of-the-mud cases into stuff that will blind you with shine. That clean, it also might cold-weld the bullet to the neck, and the primer to the primer pocket.
There's a certain procedure and rigmarole to prepping brass to get it super-duper shiny. I don't care for that either. Probably because I'm so used to my "old ways."
My brass gets tumbled (in the dirty walnut shells), then tossed on a (dirty) towel to get a lot of the dust off the tumbled brass. Then lubed and sized/deprimed all at once. The looby-reszized brass gets washed in a bucket (3 quick rinses in hot water) in the bathtub. Then it gets tossed on a different (but also dirty) towel to get some of the water off it. Then it gets laid out in old boxes (been using same boxes for over 20 years) in the basement to dry for two days. Then it gets bagged/canned and labeled.
The walnut shells get topped-off in the tumbler as some of it gets spilled during the process of fetching the dirty brass in and out of the tumbler. The dust probably isn't good for you. So, wet-tumbling does have that going for it, on account of you ain't gotta breathe tumbler dust. I been breathing it since the 80's. Probably due for some cancer from the exposure. I'm OK with that. I already done all I set out to do in this life. Well except those cases on the bench that need to be primed. I gotta get that done.