If there were general answers that would also be helpful for me and others, but here is what the activity is (I'm a senior btw): I am starting to work on what is going to be a lengthy apologetic letter to a well-known public intellectual figure, on evidence for Christianity (I think agnostic is the best word to describe him at the moment, but religion is a big talking point of his).
Of course I could try to finish it in time, but I am definitely not going to if it sacrifices the quality, which it probably would, and then I might not know about any impact it makes in time anyway. My faith is something that is present elsewhere in my application, and I could probably say that I have spent time learning about it all 4 years of HS. However it's just now that I feel ready to actually start writing.
Also I am not necessarily majoring in any subject like philosophy or theology or history, though that is possible.
As someone else mentioned, I don't think writing a letter constitutes as an extracurricular. However, if religion is important to you and you talk about it elsewhere in your application, you might mention writing the letter in passing in relation to religion being important to you, to show that religion extends past the classroom and you actually spend time working on religious work outside of school.
Writing a singular apologetic letter, whether it's 2 pages or 20 pages, is not an extracurricular activity that you can put on your college application. If that were the case, then everyone can claim that writing a letter is an extracurricular. And colleges would expect HS students to make notations on their Common App about writing singular letters, which they don't.
Extracurriculars are things you do that fall into various categories like:
High School ECs - Sports, Leadership, Clubs, Newspaper, Yearbook, Orchestra, Band, Cheerleading, Dance Team, Glee Club, Acapella Group, Green Team
Community Service- Volunteerism, Serving on Advisory Boards, Registering people to Vote, Feeding the Homeless, Caring for the Elderly and Disabled, Charity work, Fund Raisin.
Activism- Various activism on a city, state, or national level or global level.
Competitions - Science, Math, STEM, Robotics, Music, Dance, Speech, Debate, Constitutional Law, Mock Trial
Evidence of Intellectual Vitality - Joining online college course(s), taking online MOOC courses, earning certificates (life-guarding, CPR, Emergency Medical Training)
Paid Work - Like part-time jobs or consulting or gig work. Modelling on the side, tutoring younger kids for $$$, getting a paid internship.
Passion Projects - Making jewelry, selling it on eTsy, donating the money...for example.
Now if you were the Editor in Chief of a Creative Writing Journal or School Newspaper and your role and responsibilities included writing weekly or monthly articles about various subjects, including religious ones, then that's an EC. But the crafting of a single "letter" intended to convince a non-Christian to consider that you have some concrete evidence for Christianity, doesn't sound like EC but an OP-ED to be printed on the back of a newspaper expressing your personal opinion about Jesus Christ.
On the Common App, for something to qualify as an Activity, first, it has to be one of the various categories in the drop-down menu like Athletics, Debate/Speech, Internship, etc. "Letter writing" is not a category. Secondly, you have to hold a position like Member, Team-Captain, President, Board Member. Third, it has to have a formal organizational name like DECA, Model UN, ASB Student Government, Jackie's ETSY Store. And 4th you have to describe the activity in 150 characters or less.
On all fronts, this doesn't qualify as an EC. It is your individual right and prerogative to include it as one but...what happens as a result of this is your own doing.
To keep this community safe and supportive:
I appreciate it. What I was actually considering doing is putting in the position description of the EC as simply that I research religion, and putting it as a hobby, since it is not for some organization or publication or anything. It is something I have spent substantial time on throughout high school which seems to me like something to put on an application, especially since in the EC section they actually make you report the hours spent.