Okay, there's quite a bit going on in these logs. And I think I can see why this was escalated to the 14 day temporary suspension if all this happened since the end of season 6. Keep in mind, that while Riot may give you anywhere from 1-3 games worth of logs, that does not mean those are the only reports that you receive. It's simply the most recent ones that they deem worthy of sending you. The best of the worst, if you will.
Having looked them over carefully, I don't think your comment on Tumbler, or even the ones regarding the Presidential election had much, if anything, to do with your ban. If they were the only thing in these logs, I doubt you would have even been given a chat restriction. They are the sort of thing that while it might have been intended to piss people off, and it might get them to report you, it's not explicitly forbidden in the rules. The comments themselves aren't toxic. The intent behind them, and the insulting manner they are delivered in is.
I'll be quite upfront with you. Based on these logs, if this is how you talk in most of your matches, I would not want to play with you. I would mute you almost immediately. I do not enjoy playing matches with people who spend the entire time nitpicking what everyone else does wrong, even going so far as to look at their match histories to back up their insults. And MANY other players share that opinion. The "harshness" of the Instant Feedback System is a reflection on what players do not find acceptable. And if you spend much time here on the boards, you will see quite a few people who don't find comments like the ones made in your logs to be the sort that they want to see in their games.
This is not a reflection on you as a person, it doesn't mean you are bad, or that anyone here is better than you, or anything like that. Simply that many people here disagree when you say "The only toxic thing that I can find in those chat logs was a "You deserve to lose this, garbage team" in response to a bot lane duo who had been cussing and ping spamming everyone else all game."
So, as you already seem to be aware, there are four punishment tiers. 10 game chat restriction, 25 game chat restriction, 14 day temporary suspension, and permanent suspension. What you may not know, is that once you are at the 14 day suspension, your next punishment will be a permaban, if you have not dropped down to one of the lower tiers. You drop down a tier based on not receiving reports and being flagged for negative behavior in the system. The numbers vary based on how many games a player plays, and I've seen estimates from 1 month to 3 months to drop a tier. (One month obviously for players who play more games with good behavior.) I've seen it go as long as 7 months between the 14 day suspension and the permanent suspension. At this point, you will want to be on your guard, and try to avoid making the same mistakes.
I'll outline below the sorts of things that might have gotten you reported. I'm not saying all of these comments are report-worthy by themselves, but taken into context over the course of a game, they did lead to it. For your sake, you might want to watch out before saying things like this in the future.
Insulting/Verbally Abusing Teammates/Enemies: Whether they are playing poorly or not, whether they are being toxic or not, your saying so is not going to help your team win the match. It contributes nothing of any value to the match. So, for much of this chat, there's really no reason to say it.
Gamemod: begs for mid and does garbage
Gamemod: you're just boosted to bronze
Gamemod: nah she's toxic and refuses to communicate
Gamemod: she's been toxic since lobby lmfao
Gamemod: ahri is a dick and intent
Gamemod: cussed everyone out because she wanted mid
Gamemod: cant take someone who puts tsm in their name seriously
Gamemod: and doesnt even know how to eq on jayce
Gamemod: jayce comes back with that amazing comeback
Gamemod: jayce doesnt even know how to combo gate and blast
Gamemod: coming from the person who got fed off the intenting ahri
Calling for reports: The others have already covered why calling for reports repeatedly is considered harassment, so I won't go into it further.
Gamemod: report ahri after this
Gamemod: report ahri
Political Inflammatory Speech: Your intent seems to be to irritate or piss someone off. And it worked. There's nothing wrong with discussing politics in matches, but again, if it isn't going to help your team win the match, and is only going to be done in a snide, insulting manner, then it may garner reports.
Gamemod: you sound like someone who voted hillary because you needed a safe space
Gamemod: it's going to be funny when they realize that trump just won the presidenc
Gamemod: and that their safe space culture is dead
Stopping to View Outside match Histories: Why did you stop in the middle of the match to look up Katarina's match history, only to begin throwing it up as the reason why she wouldn't want to report Ahri, who she clearly beat in lane? As a teammate, I would have been highly annoyed at you for taking that much time out of a match when it could be better spent trying to actually win.
Gamemod: oh shit look at kats match history
Gamemod: no wonder she wont report ahri
Gamemod: riv, look at kats match history
Gamemod: you'll understand why she doesnt want to report the person who gave her a break
Gamemod: gets so desperate he has to pretend he's shiptur
Gamemod: kat looking at your match history again i know why you're happy
Gamemod: but i understand
Gamemod: yo watch kat go back to the losing streak after this
Hatespeech: While this may have been said to a friend, the Instant Feedback System works off a chatbot, that scans for keywords. And racial slurs are high on the list of keywords that it looks for. Using them is an easy way to get escalated up to a higher punishment tier. Even if you are not using it in the context of a slur, if you get a report in the match, the bot will see that slur.
Gamemod: riven called me a kike
Needless Insults from Games 2 and 3:
Gamemod: how much did those bronze accounts cost
Gamemod: oh mb you're bad
Gamemod: lmao you're not getting blue
Gamemod: because you're not good
Gamemod: this is why tumblr is bad kids
Gamemod: not ganking a top laner who doesnt know what to build vs trynd
Gamemod: never understood the bronze mentality of omg u used flash 2 kill me haha ur bad
Gamemod: im the only good player on this team
Gamemod: you all deserve to lose this
Gamemod: garbage team