The て
preceding 綺麗事 is the て-form of the auxiliary verb いる
. Dropping the い
in ている
is very common in colloquial speech, I.E. 思ってる
. This just gets slightly more confusing with sequential て-forms. You might think of it like this:
思う ー> 思っている ー> 思っていて。。。 ー> 思ってて。。。
In this case the second て
is just there to let the person continue their sentence. So for the sentence below
泣けばいいと思ってて綺麗事ばかりな主人公にイライラする
A very, very direct translation might look something like this:
(They) think it will be fine if they cry and are all superficial positivity, which makes (me) angry.
As for イライラする
, it's certainly a mimetic. mimetic+する
is a sufficiently common pattern that I don't think if I would call this a "verb based on a mimetic" as much as just a normal mimetic; the する
here just describes the action of being in the state associated with the mimetic.
Edit: Please note my original interpretation of the sentence was incorrect as I misinterpreted the omitted subject for 思う
. I'm using naruto's provided translation here
The protagonist thinks weeping solves everything and just talks about ideals, which pisses me off.