I'm not interested in where or when these things were practiced, only when we have a record of them being criticized.
At the moment, I think circumcision controversy is older.
440 BCE, The History of Herodotus by Herodotus, written 440 BCE, translated by George Rawlinson:
They practise circumcision for the sake of cleanliness, considering it better to be cleanly than comely.
There are also later documents where Roman and Greek writers presented anti-circumcision views (even laws), but I haven't seen anything newer than Herodotus.
There are references online to a difference in the teachings on breastfeeding between the Jewish Talmudic teachings and Islamic teachings, specifically that Jewish tradition allows the substitution of animal milk and Islamic tradition does not. It looks like a clear endorsement of breastfeeding from both primary sources:
~460 CE, Quran, The Cow, 2.233:
And the mothers should suckle their children for two whole years for him who desires to make complete the time of suckling; and their maintenance and their clothing must be-- borne by the father according to usage; no soul shall have imposed upon it a duty but to the extent of its capacity; neither shall a mother be made to suffer harm on account of her child, nor a father on account of his child, and a similar duty (devolves) on the (father's) heir, but if both desire weaning by mutual consent and counsel, there is no blame on them, and if you wish to engage a wet-nurse for your children, there is no blame on you so long as you pay what you promised for according to usage; and be careful of (your duty to) Allah and know that Allah sees what you do.
~500 CE, "The Talmud and Human Lactation" (page 4) states that Tractate Ketuboth 65A (also spelled Ketubot or kethuboth) in the Babylonian Talmud justifies an "alternative to the desired breastfeeding from the natural mother is either a wet nurse, animals such as goats, or in extreme circumstances even nursing from a non-kosher animal." However, the only relevant text I was able to find was in 60a, which mentions that both human and non-human milk may be considered neither clean nor unclean, and that the milk of a clean animal drunk directly from the animal can be helpful for some illnesses. (Talmud Mas. Kethuboth, page 242)
The verse that you link to in the Quran is in the context of child support in divorce cases. Read the parts before and after.
It is saying that children under two who are still breastfeeding must stay with their mother and must be supported by the father. It's not saying to shoot for two years, but rather that the mother can't get additional support by nursing forever.
Anti-breastfeeding wasn't a thing until formula was invented in the 20th century. Prior to that, all babies had to be breastfed, babies did not thrive without it. And the vast majority of cultures in the world didn't use milk from herd animals, so the only milk available was human milk. "Wet nurses" who breastfed the babies of other women who for one reason or another could not breastfeed, have existed for a very long time, but there was no option other than that. When baby formula came along in the 20th century, marketing guys went to work convincing people that formula was better than mother's milk, because babies gained weight faster with formula (which is true). This rather quickly saw women abandoning breastfeeding in order to feed via bottle, because it's a lot more convenient, since women breastfeeding in public was frowned upon, even criminalized in some places.
But in the wake of the widespread adoption of formula, people started noticing problems babies were having who had been bottle fed. This was especially noticeable in the third world, where mothers would feed their babies formula mixed with local water, which was often dirty, and babies could die from exposure to dirty water. It was then that a campaign began (late 60s, early 70s) that has grown greatly, that supports breast milk feeding as the best way to raise a baby.
Circumcision, on the other hand, has been around thousands of years longer. But it was more of a religious issue than the life or death issue that breastfeeding can be. The anti-circumcision movement really only took off in modern society after circumcision was adopted and promoted by pediatricians for all babies.