Many Maine Coon breeders have a clause in the contract when you buy them to say they must be indoor cats only, although some breeders are ok with it. We have a Maine Coon who is a breeder rehome (she didn't take to motherhood very well). We got her at the age of 2 years old and the breeder was happy for us to let her go outside as we live in a quiet leafy suburban area. We were worried about letting her out to begin with, especially as she was already 2 years old and not used to the big wide world. We bought a Tractive GPS collar which I found really reassuring when we first started letting her out - it does tend to have brief very inaccurate readings when you first turn it on or it first reconnects with the satellite, but once it settles down we found it extremely accurate (if she didn't come home of an evening I could walk down the road and know which neighbours front garden she was in, for instance). We used it for the first 6 months and then realised she wasn't roaming far at all so we have felt comfortable about letting her out without it for the last couple of months. The downside of the trackers is they are fairly bulky (it did cause knots in her ruff) and you have to remember to keep recharging them overnight. I found it worthwhile though - possibly just to stop me worrying. Obviously it does nothing against the risk of cars or dogs or even theft really though.
I have had conversations with several people who, when I've mentioned I have a Maine Coon have said something along the lines of "oh my, neighbour/friend/sister had one" and then paused and added "...but it got stolen" (why tell me that?!?) So I do think the worry about theft is valid. Our girl isn't very big for a Maine Coon and I think perhaps it's the huge impressive ones that might be more desired and targeted for theft. She is also very nervy and flighty with people she doesn't know, whereas many Maine Coons are said to be very friendly and trusting which perhaps puts them more at risk of being grabbed.
There are always risks to letting a cat out of course, and it's a case of weighing up how you feel about those. When we bought our house we only considered houses well away from main roads because of our cats. I don't think I'd let a cat out if I lived on a busy road, but I made sure I didn't live on one for that reason. A cat can still be hit by a car on a quiet street of course but it does feel a lot less likely.
I went out to call our girl in during the summer and to find her being chased down the road with a springer spaniel hot on her heels - it chased her right up our driveway and luckily she made the leap over our 7 foot high fence before the dog could get to her. It did really shake me up though.
Having said that, our other cats have been a rescue Maine Coon who lived to 14 years old and our old ginger moggy who is still going at the age of 15 - they've been going out for their whole lives with no mishaps and I feel their lives have been greater and happier for it.
If I'd had a cat who'd been hit by a car or killed by a dog I'm sure I might feel differently though.
We kept our girl in for the first 3 months (as in the first 3 months after we got her, she was already 2 years old) and she was very very active in the house, needed someone to play with her all the time to be happy. As soon as we started letting her out she calmed right down and just seemed more settled and content. She loves being outside and chooses to go out as often as possible - chasing insects in the grass, trying to fish frogs out of the pond, watching birds and passers by, laying in the sun, even mooching around in heavy rain - she so obviously loves it that personally I feel the enrichment to her life and happiness is worth the possible risk. Also, in my personal situation, we have a household always coming and going, children leaving doors open, running in and out of the front and back garden - keeping a cat inside just wouldn't be realistic for us (it was hard enough for the first 3 months) - so I'd prefer she is familiar with her surroundings, rather than have a cat who you try and keep indoors and then darts out and gets lost because they don't know their environment. Many people with Maine Coons do use catios or have cat proof fencing around their garden and that seems to work well for them. I knew it wouldn't work for us because there would be no way that I could also police the front door to stop escapees.
It's a difficult one (and highly emotive if you look on Maine Coon groups online)