Question: I work with a group of developers in a company having about 1000 employees. 
A transgender person who identifies herself as a woman has joined our team. 

* She gets upset when we use masculine pronouns (such as "he") to address her, which we obviously do out of habit.
* She also insists on using the ladies toilet, which makes our female coworker uncomfortable.

Taking this to HR is extremely delicate, as they might think we just don't like LGBT people. While we don't want to discriminate against a transgender person, her needs cause issues for us. 

How should we handle this situation?

Answer: 
If a person changes their name from "Jake" to "Richard" then they expect to be called "Richard" from then on. If you insist on calling this person "Jake" because he's just "a Jake pretending to be a Richard" then that would be considered quite rude.

You may not understand the reasons for the name change or think they're silly, but it's their name. Not yours. You don't *need* to understand it.

Of course, few people will get angry if you accidentally call them "Jake" out of habit, especially not if you appear to be making an effort in calling them "Richard", but the language of your original posts (before it was edited) suggests you're not making much of an effort: you use "he" consistently, and you say this is "a man who pretends to be a woman".

I'll be clear, I don't fully understand transgender people either, but that doesn't mean I won't accept them as the person they are. Sometimes you just need to shrug it off.

Clearly there is already an adversarial situation. My suggestion would be for you and your team to take a deep breath, accept that this person is different from you in ways you don't understand (or even like), and simply use "her" consistently. It's the polite and professional thing to do.

It would also help if you would actually talk to this person – possible with someone from HR present – about how *she* feels about this. It can be easy to forget other people's emotions when you're involved in a conflict.

As for the other issues (bathroom, "unnatural chitchat"), talk to her. Talk to HR. Find a solution you can both live with.
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> How to deal with this situation?
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People get to self identify, you get to respect that and act professionally and that's it.

People are tied to their identity. It's literally how they define themselves and it's important to them. Imagine it were their religion or political views if that makes things easier for you.

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> such as getting upset whenever we use the pronoun "he"
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I recommend you apologise for referring to a person in a way they found offensive and to correct yourself, as well as make an effort to improve.

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> also demands to use the ladies toilet, which makes our only female coworker quite uncomfortable
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If your female co-worker is not feeling comfortable or safe in her work environment that's something she should bring up to your HR department since that's something that a company should decide and not you.

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As a kind reminder, you don't have to be friends with everyone at your job - if you don't like that person the best thing to do would be to act professionally and also minimize non-professional interaction.