Churches will be reluctant to allow non-members use of their organ to learn on.
Some general observations from someone who has a degree in organ and has been playing for many years.
I love the organ and its literature and always enjoy sharing the instrument with others. But getting access for non-staff or, especially, a non-member can be a logistical challenge. Keys, building access, and personal safety (for you as well as others) are just a few of the considerations.
The best thing would be to befriend the organist and show your seriousness, trustworthiness, and respect for the instrument and institution. Better yet, take lessons from him/her. Often, you will be allowed to practice on the instrument where you take lessons. And the lessons will speed the development of your organ-specific technique.
If you do gain access, here are a few points of etiquette to bear in mind:
1. Consideration for others: If there is church staff present when you come in, let them know you are there, why you are there, and how long you'll be there. There may be something on the church's schedule you don't know about. If you play loudly (that's part of the fun, isn't it?), just remember they can hear you down the hall. If you are prone to shouting expletives when you mess up, try to refrain from that. There is no such thing as "private" organ practice at a church.
2. Bench: Never stand on the pedals when getting on or off the bench or adjusting it. To get on, sit on the end of the bench, then, using your hands, rotate forward and slide to the center while keeping your feet off the pedals. If you adjust the bench, do so while standing on the floor. Make a mental note of the position (height & distance from the keyboards) before you move it, then put it back when you leave.
3. Shoes: Many (most?) organists, including myself, use dedicated shoes for playing. You don't need to do that, to start, but don't use your street shoes, especially if they have black rubber soles. Until you start seriously working on pedal technique, house slippers (without rubber soles) or even sock feet are OK.
4. Don't change the pistons (preset combinations). Nothing will get you banned from the instrument faster.
5. Organists become accustomed to practicing in less than comfortable conditions. Usually at off times, heating is run lower than normal and air conditioning (if there is any) is set higher. This is for economy. It also makes the organ more out of tune. You just have to deal with it.
I hope all this isn't too off-putting, but these are things that conscientious organists do all the time at their own instruments and when visiting elsewhere. Observing these things will help you continue to be welcome at the organ.
Learning the organ can be a lot of fun, and can open a whole new world of music.
Best wishes on your new musical adventure.