I have had to set a DMV on my router and other backend network changes. No change on ability to play with friends. This started happening last week when I tried to play with my gf on a lan style network. Game was constantly kicking me. I changed games and didn't have any problems untill my gf started to play on her PS4 again. Why are these problems just now happening? Destiny was a social game for me and now I don't have any reason to play. I don't like solo grinding so if I do not get to play with my group, I get bored and stop playing... Oddly Trump news is more satisfying than trying to play destiny with all the problems I'm experiencing.
When more than one device is accessing Destiny 2 from the same household, UPnP is required. Since you don't mention whether this is the case or not, I'm assuming it could be. Important with UPnP is that you don't have any port forwarding enabled at the same time. NAT Type 2 does not prevent you from playing the game at all. I have NAT 2 and can play all activities fine.
Clarifying, my gf and I stopped playing because we couldn't finish a strike with the baboons, weasels, and one other problem saying it was an isp problem. She had logged out then re logged in once she got bored. Upon doing do, I was given network errors on my PlayStation and removed from online play in Dark Souls 3. Destiny is the culprit based on this experience.