How does a Christian reject another's theology without rejecting their faith?

I think this is more a matter of character and imagination than anything else. George Macdonald is the best example of someone who is able to represent characters sympathetically with whom he has profound theological disagreements. (I don't know what he was like in life, but it's everywhere in his novels.)

Here is a passage from Robert Falconer:

But while such a small portion of the universe of thought was enlightened by the glowworm lamp of the theories she had been taught, she was not limited for light to that feeble source. While she walked on her way, the moon, unseen herself behind the clouds, was illuminating the whole landscape so gently and evenly, that the glowworm being the only visible point of radiance, to it she attributed all the light. But she felt bound to go on believing as she had been taught; for sometimes the most original mind has the strongest sense of law upon it, and will, in default of a better, obey a beggarly one—only till the higher law that swallows it up manifests itself.

Of course the idea behind it is that God is present and active in ways that we don't necessarily understand; and that taught Macdonald humility, at least.

If you had asked, "How does a Christian resist another's theology without resisting their faith?" it might become obvious that that would be impossible. To resist the theology of another requires (a) knowing why you (the Christian in this case) has to resist this other theology, and (b) knowing at what point the other's theology is incompatible with Christian faith.

Please note that, in principle, the other person here could be a Muslim, an agnostic, a Hindu etc, and not necessarily a professing Christian. However, you are asking this question in the Christianity site, and restricting it to Christians. The difficulty is that every person claiming to be a Christian sincerely believes that is the case. You won't get a person publicly stating, "I'm a Christian, but not actually; I have no belief in Jesus Christ, or in God, or in anything the Bible says, but it's convenient for me to pretend to others that I'm a Christian." Such people actually do exist but I doubt if you will find any of them participating on this site!

The simple answer is that theology is what a person believes to be true regarding God and worship and living as a Christian; faith in the sense you ask about is personal to the individual. It is not up to me to reject another person's faith - indeed, I cannot do that! Only the person with a particular faith can decide to reject it. I can disagree with their theology (or some aspects of it) without rejecting or resisting the person. However, if I come to see that a person's beliefs and/or practices are heretical or apostate (according to what the New Testament states), then I would have to have nothing more to do with that person. That could be viewed as resisting the person because of their faith.

There is a lot of overlap in the beliefs of the various nominal Christian denominations, which makes this a difficult question. It might be better to step back and ask yourself a more extreme and therefore easier version of it first.

Ask the question about Hindus or Buddhists or other non-Abrahamic religions instead. Many members are very devout and faithful (some to the point of death). They may be very sincere, but you will see them as sincerely wrong.

Get a good understanding of those situations first:

• Understand why they believe what they do (family tradition, personal religious experience, study and research, …).
• Understand why you disagree with their various beliefs (e.g. because they are false, or because they are true but incomplete).
• Understand how you feel when talking to these people (barely tolerating them, wanting to convince them they are wrong, pitying their ignorance, …).
• Understand how they feel when talking to you.
• Understand your motives for talking to them (for better understanding, to convert them, to ridicule them, …).
• Understand your realistic expectation of results from talking to them (potential changes in you, them, or both).
• Repeat until you become comfortable with the situation.

Only then should you apply what you've learned to your interactions with members of other Christian denominations.

In essentials, unity; in nonessentials, liberty; in all things, charity. - Rupertus Meldenius.

This idea is spoken of in many ways, but they all have the same big idea: there is a core of Christian theology which is essential and must be upheld without compromise, and a periphery for which diversity is allowed and even encouraged.

While there is considerable debate over which doctrines should be really considered essential, there is also a broad consensus for some central doctrines. Numerically, most Christians (Trinitarians) consider the Nicene Creed to be the most important doctrinal statement that unites true Christians and separates them from the heretical churches who cannot uphold the entirety of the Creed. Conversely, many non-Trinitarians (and the non-Nicene Christians who consider themselves Trinitarian but differ on some details) would consider the theology of the Nicene Creed to be heretical, and so it marks out a boundary respected by most people on both sides of it.

On the other hand, there are issues which pretty much no one would consider to be essential; things like musical or liturgical styles, church governance models (like whether you have one leader at each level, such as a pastor, priest, bishop, etc., or a plurality of equal elders), or whether a small group that meets to study the Bible and pray together should be called a Bible Study Group, a Home Group, a Cell Group, a Community Group, a Gospel Community, a Life Group, etc...

But there are things that most of us would say are far more important than the trivialities (what colour carpet to install) but are not essential either. It's helpful to have a third category: things that are necessary for cooperation in Christian ministry and mission. For example, Protestants say that there are many faithful Christians in the Catholic and Orthodox Churches; they don't think that only Protestants are saved or only Protestants are True Christians. But the doctrines of the Five Solas are considered very important to Protestants, as they concern our understanding of the Gospel and refute several distortions of it. Because of these differences, Protestants and Catholics usually don't cooperate in evangelistic projects; when a core task of evangelism is to explain the Gospel, it's hard to work together at that task with people who think of the Gospel in very different and sometimes contradictory ways to you. (This doesn't mean that Protestants and Catholics can never work together; for example, they often sponsor Bible translation projects together.) Similarly, those who support women's ordination and those who oppose it would likely have many issues if they tried to work together in a church planting organisation. And this is also why almost all denominations pick a side in the infant baptism debate rather than being deliberately agnostic about it; as a sacrament, baptism is one of the most important things of the Church, and most Christians consider it important for churches in their denomination to have a consistent position on the sacraments even if they differ about many other things.