Are we freer than the people of the World State? Are there ways in which we are conditioned, too?

You ask two questions and it will be easier to answer them separately.
Are we freer than the people of the World State? Yes. Although there are many interesting similarities between modern life and Aldous Huxley’s fictional World State, the genetic predestination of embryos in Brave New World removes even the possibility of freedom.
In the two opening chapters of his novel, the fictional Bokonovsky’s Process is presented. In this scientific advancement, a single, artificially inseminated egg can produce up to 72 identical individuals. These babies are raised not in the womb but in test tubes. They are not born; they are “decanted.” The purpose of this process is described by the Director of Hatcheries as a major “instrument of social stability.” Bokonovsky’s Process enables social stability because it facilitates the creation of a genetic caste system, where an individual’s intelligence, aptitude, and even height are predetermined.
The World State in Huxley’s novel has become God by determining the fate of individuals before they are even conceived. There is little possibility of free will when only Alphas and perhaps some Betas even possess intelligence. The rest of Huxley’s fictional caste system are doomed to a life of drudgery and mindless entertainment because their genes do not allow for anything else.
In Huxley’s novel, propaganda conditioning is used to reinforce these genetic predispositions. Beginning in the test tube and continuing until death, the citizens of the World State are inundated with axioms that encourage sexual liberties, excessive entertainment, and abundant soma use. Lenina’s character is a particularly good example of this, as she cannot help herself from echoing mindless slogans such as “a gram is better than a damn.” Lenina retreats to these maxims in moments of stress or discomfort, which highlights the effect of the relentless propaganda machine created by the World State to eliminate individual freedom through pleasure.
The freedom of the citizens of the World State is so restricted by genetic predestination and conditioning that they are not capable of comprehending their own captivity. While entertainment and impulse-driven behavior dominate Western culture today, nothing approaches the loss of individual freedom depicted in Huxley’s novel Brave New World.
Are there ways in which we are conditioned, too? Yes. All humans are conditioned in some manner or another. According to the Oxford English Dictionary, psychological conditioning is the “process of training or accustoming a person or animal to behave in a certain way or to accept certain circumstances.” Children are conditioned to be polite. Students are conditioned to raise their hands when they want attention. Adults are conditioned to arrive at work on time. Conditioning is necessary; it certainly isn’t inherently evil.
However, Huxley suggests in Brave New World that the power of conditioning could be harnessed for nefarious purposes. He warns that the easiest way to condition a population to voluntarily surrender their freedom is to offer pleasure. Perhaps this is why so many consider Brave New World to be so thematically relevant today. As the media-driven culture of short-term satisfaction becomes increasingly all-consuming, Huxley’s novel forces us to examine our own lives and examine what freedoms we surrender voluntarily in the name of happiness. I hope this helps!