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: 
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First, you should try your best to **address this person with the pronouns they prefer**. I know that this may be hard, especially for people that are not used to working with LGBTX people.

Now, regarding the bathroom, I think that this is something that has to be sorted out with management or HR, as you and your coworkers are not in a position to determine how company members should use the bathroom. 

The ideal thing would be to have a **gender-neutral bathroom**, so this person can use it freely and comfortably. But, in case you don't have one, I feel that this situation *has* to be taken to HR or someone in position of deciding these things. 

No need to *"be perceived as discriminatory"*, as this is a valid concern. This situation has to be phrased something like *"We need to define the use of our bathrooms for any gender identity"* so it is not perceived that way.
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