I liked Shiphtur and ZionSpartan playing for the team when they were promising newcomers and had that kind of reputation. I liked GGU for being a self made team of newcomers as well and back then I liked Mash too, because he consistently had very good farm and seemed capable of winning even on low damage champs such as Graves (which he played a lot of back then). After that I was rooting for Sheep, wanted to see where Impaler can go, and wanted Cris to prove the haters wrong too.
I still don the icon because like I described above, I don't want to change teams based on big wins. I don't hate anything about Coast either, so there's nothing pushing me to drop them. I dislike a number of things about CLG, TSM, FNC, TL, SK. EU LCS has never been very compelling for me even though I'm from Europe myself.
In addition to that what keeps me from dropping Coast is that I think even in spite of their performance as well as management which on the surface appear to be questionable, I don't think neither the team nor the players have reached anywhere close to their potential, and I think they're getting an unreasonable amount of hate.
The only thing that discredited them in my eyes is that one moment where they brought in ringers and dropped Rhux and co. Santorin wanted to leave for TSM, nothing they can do. Mash lacks the confidence to be an effective ADC - that's the only member of the team I don't have hope for. For all the other guys I can still see improvement, though it would depend a lot on management and coaching, getting good picks and bans, just getting better as a team and most of all keeping spirits up, which I don't think they managed to do. It looks like their play suffered a lot with each loss they accumulated.
I'm pretty hyped for NME. If they manage to play well enough and stay in the LCS, I might switch to them, unless some negative aspects around their personalities come to light or something like that. TiP is likeable from where I stand too, but I don't know who they are just yet. Next split is going to help determine that. Dignitas I want to like, but Odee is rightfully being called out (though people go way overboard with the hate here too) for failing to find a proper jungler and coaching staff for the longest time.
That's basically it, I think. I could list all the things that make me not switch to the big teams I listed first, but you didn't ask for that, so I skipped it for the time being.