Generate the answer for a given question. The question requires common knowledge of English. Make sure that the answer is in detail, long, consistent with the context, and requires general knowledge of English. To be less repetitive, please vary your language for each question. Give a proper explanation to answer, and if necessary, provide the definition of various terms. And conclude your answer if it's long. If you have used other resources (e.g., Merriam Webster's.) to answer the question, include citations in your answer. You don't need to paraphrase the context of your resources, but make sure that your answer is consistent and complete.

I recently had somebody tell me that a mutual friend of ours who is genderqueer prefers that people refer to him/her using the gender-indefinite pronoun they. In some cases, this almost seems okay: Kris left their umbrella at our house. On the other hand, if Kris is sitting right next to you, it feels very odd to say They (meaning just Kris) would like more cake. Or even odder, Kris would like some more cake, can you please pass it to they/them?' Are these usages grammatically correct? Are they in the process of becoming grammatically correct? Are there more correct alternatives?.
I think the reason for your friend's preference is that using either the male or female pronouns implicitly pigeon-holes the person in question as either one or the other. However, all of the examples you give seem to me to be forced, and to shout out loud 'Hey, look at how sensitive I'm being! I'm not calling Kris either male or female!' There are sensible alternatives to all of these examples that do not break any grammatical rules. 'Kris left their umbrella at our house' : Kris left an umbrella at our house (yes, it could technically then be somebody else's umbrella that was left behind, but would you really know?) 'They [Kris] would like more cake.' : Kris would like some more cake. 'Kris would like some more cake, can you please pass it to they?' : Could you please pass the cake? Kris would like some more. While my dictionary (Chambers 1990) does have a secondary definition of 'they' as 'he or she', it also says that this usage is 'with pl. verb', as in 'there are lots of people; they are happy'. 'They is' would not be correct.