I'm assuming that by "naturalism" you mean the view that the physical world is all that exists, and that we have no immaterial self/soul. In that case, I don't think it's possible to have free will because our brains, being part of the physical world, obey the laws of nature. Every thought or action that we have is determined by the physical processes of our brains which are determined by the laws of chemistry and physics. There's no room for free will.
If I can be presented with a situation where two (or more) choices and the laws of science don't dictate that I will choose either then the reason for my choosing of either must be something outside of the laws of science. If there is something outside the laws of science then naturalism is false, if there is nothing outside of the laws of science then free will is an illusion. Both can't be true, not in any logical way of thinking at least.
If our thoughts are just illusions of a material process -- that is, the motion of chemicals in our brain -- then it seems that there is no possible way humans have freedom of the will. If naturalism is true, then by definition, nothing operates beyond the laws of nature. And if nothing exists beyond the laws of nature, then our thoughts obey the laws of nature. And if our thoughts obey these laws, then free will in the way I understand it doesn't exist.
We all instinctively believe in libertarian free will in some form (not to be confused with the political ideology). A simple argument is as follows
1. Naturalism allows only determinism or naturalism or some combination
2. Random will is not free will
3. Determined will is not free will
Even if you are a compatabilist you still need to believe either that naturalism is false or our day to day experience is illusion
Will, and intentionality are explained away on naturalism, not explained by it. Even if it were the case that naturalism could be true in a non-determined physical universe (where probabilistic interpretations of quantum hold rather than deterministic), then naturalism so defined must still contend with the existence of a will.
The question is posed because it is saying that naturalism claims the events of the universe are deterministic. That is, everything was somehow set in motion and now they are just playing out. If that is the case, then free will must be an illusion; when you make a choice, believing it to be your free choice, it is really the choice you were destined to make according to the laws of naturalism and therefore it was not your choice, it was simply what happened as a result of everything before it.
As Sean Carroll, a naturalist, stated in a debate with William Lane Craig, humans have free will because we do not yet have the scientific knowledge to understand what composes our decision making. The implication is that once we have complete scientific knowledge we will be able to determine our decisions through scientific analysis. This makes the naturalistic view of free will an illusion, not true free will.
Naturalism means that all activity is the result of laws of nature acting as they must at any time. In particular we have no power of any kind including "choice" Moreover, we can have no knowledge of these laws without a nesting of self referential recursions, since we are a product of them. Such a knowledge would lead to paradoxes meaning the laws would be true if and only if they are false. This is the main problem.
This is another way of stating the difference in believing in God or not.
The naturalists tend to follow the idea of the natural man. The Free Wills tend to follow the supra-natural way beyond nature and science.
We are not as rational as we thought to be.
You either believe in substance only (scientific approach) or you believe in God and know that there is more about life and the universe than just matter and its natural laws.
The physical world is governed by physical laws. Physical laws are not subject to our discretion. They operate beyond our governance. What is beyond our governance is not free. Free will can only exist if exists beyond the margins of the physical world. Since free will is a lived experience it's existence can not be reasonably questioned any more than our experience of colour or sound.
You get one life to live. So use things to your benefit. It's fine to believe something because of the benefits it provides rather than because the facts suggest it is true. Determinism doesn't work for me. I will sit around and do nothing because what's the point if nothing is chosen. Free will is therefore functionally correct for me whether it is factually correct or not.
Just because it is possible to determine what their choice is going to be does not take away their free will. If you are going to make a choice, does it matter if there is a chance that you could have made a different choice? Since people do make choices, and you do have to make a choice, then the choice that you are going to make already exists in the future, so it is impossible to make a choice independent of the laws of physics. In any case some process must have come behind making that choice, that is to say, that it is not totally random. For example, if I was going to offer some kids ice cream or vegetables, I could say for certain that they would all pick the ice cream. But does this take away their free choice? No. I can know the process that is going on behind the scenes to make them make the choice. They want the sweet flavor. Therefore choices are deterministic. I can also predict the decision I am going to make about a future situation with a higher degree of accuracy, since I know my self.
For someone to subscribe to both the idea of naturalism and also to the concept of free will is in no way contradictory. A person is free to believe in what they want and to choose theories or thoughts that are in line with their beliefs. Who are we to judge people.
Naturalism is about how the universe and cosmic things around us effect our world, free will is the right to make a choice, and see who that choice effects, and how they react to that choice with a choice of their own. Nothing really to do with each other that I can see.
I interpret naturalism as being concerned with the world around us and it's karmic functions, while free will is expression of one selves upbringing, beliefs, and though processes through their own actions. Furthermore, I view both naturalism and free will and complimentary units, as easily working side-by-side in a very functional fashion.
No it is not contradicting naturalism because being natural involves free will. Being natural does not mean being perfect and people will make mistakes no matter how hard they try not to because they are imperfect but that should be considered natural because everyone is part of nature and we would not be able to make mistakes if we did not have free will.