who will rid me of this troublesome priest

the story goes that when Thomas Becket opposed King Henry II's policies, he cursed and said who will rid me of this troublesome priest.(Pope Francis is mad, according to the gossip or fake news going around the trad blogosphere).

what are they angry about?

Because Pope Benedict and Cardinal Robert Sarah, an African priest best known for his books on the search for holiness, have put out a book about the priesthood that agrees with Pope Francis' "official" comments but are highly critical of the slight of hand he is planning in the "Amazon synod" document coming out next week. 

This is a very serious thing: Because as Pope Francis and his minions keep pushing reform (i.e. deforming the traditions of the church to fit the PC modern world), the dissent has expanded from the far right Trads to the ordinary pious believer (but not the mediocre types in the pew who don't read about such things of course).

How bad is the kerfuffle? 

Father z has a summary of the kerfuffle about Pope Benedict and Cardinal Sarah's book, and refers you to Edward Pentin's article for a timeline refuting attacks on it as fake news.

Summary? Someone is telling the emperor he has no clothes on: that the entire Amazon synod was not a grass roots movement but an astroturf conspiracy by the radical PC theologians

This sounds like Cardinal Sarah, who grew up in a small African village and knows a bit more about "indigenous" people than German theologians behind the astroturf:

...I believe that these topics are the obsessions whose source is found in the milieus of university theology departments. We are dealing with ideologies developed by a few theologians who, like the sorcerer’s apprentice, wish to utilize the distress of poor peoples as an experimental laboratory for their clever plans. I cannot allow myself to let them act freely in silence.

and it's about more than if married men should become priests: it is about the meaning of the priesthood, and the holiness of the church.

It is pushing back the idea that the church's aim is to push the green agenda as the main aim of the church: as opposed to the idea that the church should nurture people in holiness:

here he, presumably the good Cardinal, pushes back against Pope Francis' plan to make the Eucharist something for all, implying it is merely a feel good symbol.

One receives the Eucharistic presence with wonder and joy as an unmerited gift. The believer who claims it as due to him demonstrates that he is not capable of understanding it.

the hysteria about the book hints to how this is a serious matter, and maybe another step toward schism in the Catholic church. If this happens, it will have geopolitical implications that no one wants to discuss.