I would argue that the materialistic worldview is necessarily deterministic.
If the kind of materialism you're talking about is monistic and therefore logically consistent with the premise that only matter exists, yes.
If determinism holds true, then every choice we make could not have been otherwise.
In Marxist Materialism, whilst all our actions are caused that does not mean they could not have been otherwise. What counts is whether something we necessary or accidental in relation to the process. Certian keys aspects of our decisions remain consistent if the same decision is repeated and are therefore necessary to that process. However, there are certain circumstances which can change when the decision is repeated and whilst these do have an effect they do not change the outcome.
e.g. In the case of a marriage ceremony it doesn't matter which church I go to, as so long as it is the same denomination the ceremony will be the same. in that respect the religion necessitates a certian kind of ceremony, but the choice of location is an accident in relation to it.
Regardless on how you define "free will," it must be compatible with either determinism or indeterminism.
This depends on what you mean by 'freedom'. Metaphysical or libertarian free will assumes that freedom is a property of the mind. it is based on dualistic theories that we can chose to do something irrespective of material constraints because the mind and the body are assumed to be seperate. Taken to its logical extreme, this is false; e.g. I cannot 'will' myself to levitate off the ground and am therefore not 'free' to do so. because choice is thought to be independent of the body/matter, it is considered accidental and without cause. therefore determinism and 'freedom' of the will are mutually exclusive.
An alternative view is that freedom is the freedom to realise necessity. I may not be able to fly by an act of will, but by understanding the laws of thermodynamics and building a plane based on their specification I am 'free' to do so.
Yes, there is a third possibility. We can jettison "causality." But in so doing, we jettison free will with it. Because if an agent doesn't exert any causality whatsoever, then the agent cannot possibly exhibit free will.
In terms of realising necessity the agent is themselves the cause and therefore has freedom of the will, because will is determined. Or as Bankjanki quoted...
"Man can do what he wills but he cannot will what he wills." - Schopenhauer
This is an interesting change of affairs. You now seemed to have co-opted my view, namely, that subjectivity is a fundamental component of the nature of reality. Nevertheless, a truly probabilistic event is one that ultimately reduces to some element of pure chance. IOW, indeterminism doesn't make free will anymore palatable than determinism. This is what you and most people fail to understand.
The "problem" with materialistic determinism is that will is caused and is not the product of pure chance. This raises a series of perverse ethical problems that if we can gain objective and therefore scientific knowledge of a person we can 'predict' their behaviour and therefore control it. However, the nature of this control is not absolute- we cannot will another person to beahve one way or another, but we can condition them to behave a certian way like one of Pavlov's Dogs. Our ethical understanding relies heavily on metaphysical or libertarian conceptions of free will which emphasise subjectivity as the agency of a person independent of material constraints and causes. So this remains a relatively unexplored area of ethical understanding.