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.
There are a few "simple" things at play here.

Professional behavior, inter personal etiquette / relationships and legal framework depending on the country this takes place in.

There is nothing you personally should do, except to - out of personal courtesy - make an honest effort to use the female pronouns.

The female co-worker may have a chat with her about not being as comfortable to have chit chats in the restroom or to talk about the boys in general.

Depending on her personality, this in fact may be true.

In many countries the employer may be obligated to allow a transgender person to use the toilet of their choosing or decides to allow it to avoid appearing discriminatory.

So escalating it to HR would indeed not make sense and create a more unwelcoming work environment.

On a personal level there is someones behavior towards you and others, their interests and opinions and of course the chemistry as they say.

It is perfectly fine if you end up not socializing with each other.
Don't blow things out of proportion, these things tend to sort themselves out.

Oh, btw. many people make weird noises on the toilet. 
As long as it doesn't sound like someone is in actual pain or seems unwell I see no reason to raise a concern. 

In professional relationships race, gender, sexuality etc. are of no concern and have no place in becoming issues.
What do they bring to the table and how can that support the team or may damage the work are valid professional evaluations of individuals.

In private you may not agree with their personal choices or lifestyle but in free western societies you have no authority to question them.
It might not be your cup o' tea and doesn't have to be, said free society allows you to live your life the way you want it as well...so, yay to freedom and personal liberties I guess (8