Summary Answer
No. Not, when it comes to the doctrine of God, because from the group's vantage point, that knowledge is essential for salvation and the group's job is to lead you to salvation.
Notice that it is a different question than whether other groups who hold different doctrines of God can be saved. It depends on the group; some groups are more exclusive than others.
Notice also that the group usually will differentiate between believing God and knowing the intricacies of the doctrine of God. What the group typically asks you, especially if you are still a child, is to believe God and start praying to Him. And by joining the group you at least show a willingness to entertain and to learn the group's definition of the nature of God, instead of rejecting it out of hand.
@Ray Butterworth presented an interesting counterexample, the mainline Protestant United Church of Canada which used to be thriving but has been declining in membership and attendance: see 2013 statistics with projection for 2025 and how in 2018 the numbers seem to follow the projection so far. If this is caused by the watering down of its doctrines, then this proves my answer is correct, since by watering down too much, a church becomes more like a social group.
A Christian group's raison d'etre is to offer a theory of God
Every group will ask her members to subscribe to a certain theory of the nature of God since the very logic of the Christian salvation demands the member to take an Action based on that Theory. This is different than Buddhism / Hinduism.
Sure, it's not the theory that saves, but God through Jesus who is present now in his Holy Spirit. But salvation is a LIFETIME PROCESS, not a one time event of simply saying "I believe, X, Y, Z" and then you're saved. It's a marriage, and this requires a certain dependence on your spouse, God; the theory simply helps one to make sure this relationship leads you to the right outcome (heaven). It is like during the dating period where you are ascertaining some provisional beliefs about the NATURE and PERSONALITY of your fiancée before you are daring enough to later propose and to go through with the wedding.
If you are rational, would you go into the marriage without at least believing something about your fiancée?
Sure, these provisional beliefs will be tested and modified by your experience as the marriage turns from 5 year, 10 year, 25 year to 50 year golden anniversary. But an initial set of beliefs IS needed to take action. In fact, behind every subsequent act relating to this God, like prayer, worship, going to mass, etc., there is a theory which gives your mind the REASON why you perform that act. It's unavoidable for us humans because we are RATIONAL animal, not a being that performs only by instinct.
Thus, the group's VERY reason of being, its raison d'etre to be fancy, is to provide a member with this THEORY, backed by the kind of God that the group will in turn depend on for its authorization, a LICENSE, to be upfront with the members that the group represents God correctly. Secondly, the group will also depend that this God will perform his promises to save the members according to the theory. This theory is called the denomination's theology.
You compared it with science (see your comment below)
You don't need a theory to be perfect or exhaustive in its account of reality to be of practical use. Classical mechanics is practically useful, even though General Relativity and Quantum Mechanics are more exhaustive and accurate in their account of reality. Likewise, I don't see why you couldn't have an incomplete, imperfect understanding of God's nature and still have enough revelation to be saved.
It's true that in the beginning of your salvation journey your understanding of the theory of God you obtain from the group doesn't need to be exhaustive. A child does not need to recite the Nicene Creed and understand all the words in it. In other words, you don't have to be a theologian. But since everything practical in salvation is defined in terms of that God, it's an assumption that you must be willing to accept (by trusting the group's authority to teach) even if you don't understand it. It's your pastor/priest who went to the seminary so he/she knows how to teach the right theory of God according to the group. You just need to be open to LEARN this theory from this pastor as you mature in your faith so you can relate to your God better. But if over time you insist on rejecting this theory then the group is not for you. BUT whether you are saved or not depends on God, not the group. The group can teach, but it's God who judges. In Catholicism a criteria commonly taught is whether your ignorance is invincible.
You and the group
So in Christianity you need to get "married" to God. Notice that you don't get married to a denomination, and consequently, not to the denomination's theology. Theology is a theory about God. You are married to God, not to a theory of God. More precisely, marriage here is being "born again" by opening your heart's door to Jesus so that his Holy Spirit can enter and dwell in your heart. From that moment of conversion, you pledge allegiance to this Holy Spirit.
What's the mechanics of this "born again" action? How are you supposed to cooperate with the Holy Spirit dwelling in your heart? This is where the group comes in. The group is the broker, providing you with the theory (theology).
Theology of salvation. Theology of Christ. Theology of the Holy Spirit gifts and virtues. Theology of sin. Theology of the church (as eventually you need to have fellowship with other born-again believers). All kinds of theologies you need for your journey.
Depending on the group, they will provide sacraments. All of them will provide support group and connection with other believers, because in Christianity, you need to join a VISIBLE part of the universal body of Christ. No man is an island. Even non-Christians say that; Aristotle says that a man is a rational and political animal. In any Christian group worth its name, they will teach you John 15:1-17 as the basis for having fellowship with the group's members.
What if you're not happy with your group? Then find another one. Does it mean you sever your relationship with God? No. God is not the group. You simply switch broker. You need a broker to get started. You need a broker grow in your faith together with other believers. You need a broker to conduct your funeral rite! You just need one at a given time, since you need assurance about the right kind of God / Jesus / Holy Spirit to whom you are "married" for life.
Conclusion
Humans are rational animal. We need a good reason to act. Salvation is a matter of life and death, so we need VERY good reason. God is ambiguous, but not THAT ambiguous. A group will help make this God less ambiguous and will help us to take actions to nurture our relationship with Him. Without serving us with a theology of God and salvation, why would a group exists?
As for requiring the members to subscribe to the group's theory, it's partly a matter of social cohesiveness, but also because the group claims to teach truths coming from God who authorizes ("licenses") the group's mission in the first place !
APPENDIX: A tip to find an authentic church
How to choose a group? Any group can call themselves Christian, but how do you know which one is authentic? Those who are authentic will center their doctrinal position on God according to a certain understanding of the nature of Jesus. See Christian theology professor Roger Olson's take on this where he uses the concept of "centered set" originated by famous missiologist Paul Hiebert. The closer the group is to the center, the closer they are to the orthodoxy, orthopraxy, and orthopaty of the early church who subscribed to the Nicene and Chalcedon creeds.
:
Why Chalcedon? Because in authentic Christianity, salvation requires an action which in turn is based on Jesus being God incarnate. SO MUCH depends on this doctrine. That is why it makes no sense for a Christian group NOT to require a definite doctrinal position on God.
If we open ourselves to God, He will guide us to choose a group that is most suitable for us for our current circumstances according to His plan for us. The group will be different depending on our upbringing, our preferences, our culture, the sheer local availability, etc. But the Christian God is not tied to a locale, praise Him ! We can pray to God to lead us to the right group and possibly change to another group as we journey with God.
