Oh my. You actually made me laugh, you know? I think we’ll just move past all the strawmen in the first paragraph there (culture war on the easily threatened? war against white males? Teddy Broosevelt? Where do you even come up with this crap?) other than to say that I care so little about profile pictures I actually had to remember which one was on this when you started talking about it (also, not a drop of alcohol in that picture.)
To the core of your actual argument…is Tyrion a madman? YES! Remember, this is a series that contains the phrase “madness and greatness are two sides of the same coin.” Some of what Tyrion does is absolutely mad…self admittedly sometimes! Killing his father and former lover was absolutely a mad act, spawned out of emotional rage, and is portrayed as such. (If you think he killed his nephew you haven’t been paying attention.)
Does a madwoman turn down a thousand ships with thousands of men and a marriage proposal? Not your best example, because what could have easily happened (and still could really) is Euron getting ticked off that he was called halfway around the world only to be spurned, and subsequently using the Iron Fleet to blockade King’s Landing and bombard the coast. With very little fleet of her own anymore and no Tyrell ships Cersei would be hard pressed to defend-that’s why she needs Euron and his ships in the first place. So yeah, actually, that act is a bit mad-it might work out for her, but there’s a lot of risk and it doesn’t seem well thought out (sure, she’s at least going to test his loyalty, but calling him out there in the first place without fully explaining the pretense is mad.)
You really seem to have invented a lot of your own opponents on this one. I don’t think many people would say Cersei isn’t cunning and ruthless, but like everyone else in the GOT universe she’s flawed. The whole madness angle is part of the reason Jaime drifts further and further away from her-it’s written into the story! Denying it (and “attacking” profile pictures rather than discussing the merits of the argument at hand) just make you seem like a fool.