I too am having serious issues. If I do get in, I can go do one crafting writ and then it stops working or it boots me completely. This is bananas. Started having trouble yesterday but it is way worse today. Missing out on a lot of those anniversary boxes.
Update: so just for the heck of it I decided to try playing on wireless (hard wired before) and so far no issue. This is ridiculous
Another update: now after doing writs on two characters, WiFi isn’t working either. It’s not our internet because I can play other games.

Ha-ha! So last night I cleared saved data, and I turned off both ps4's, unplugged everything. Modem, router, ps4's. Let them all sit for about 10 mins while I folded laundry. Then plugged in my modem till that was solid, plugged in the router till that was up and wifi going. (ps4's are both wired tho) then plugged in the ps4's and turned them on.
So far, fingers crossed, everything has been good for us.