I'm also diagnosed ADHD. I've done a bit of volunteer work and a bit of casual/student type work.
TBH I think a lot of this is just volunteering. Volunteer work attracts a wide variety of people for a wide variety of reasons, some of which overlap quite heavily with not having much paid work experience, which again, can be for various reasons. But for that reason it can be a totally different experience to working somewhere that everyone is on the payroll, where as rookie says, there would be a consistent hierarchy/structure and probably set procedures. The entire organisation being chaotic doesn't implode everything as fast as it would if it was a profit making business, and it can be a bit frustrating if you can see how things could be made smoother or more efficient but someone is stuck in their way of doing things. I also think it's really common for people who work long term in volunteer organisations to be ND, whether it's because of the strong sense of justice, struggling with paid work positions, something else, or a bit of all three.
First of all I would say 3 months is not too short at all for a volunteer position if you're wanting it primarily for CV kudos. So if this is the only thing keeping you there, then go. You will have learnt some things about that organisation which you can take to future interviews etc. I don't see why you would lose a reference? They're not going to say something horrible about you. Most references these days are literally just "Yes X worked here between these dates and was not fired". You can make up any excuse at all to leave whether you say it's just not a good fit for you, or you have too many other things going on right now and need to let this one go, or make up another position (or actually get another position to go to).
OTOH it might be a useful thing to persist, in terms of gaining experience in dealing with a situation which is not immediately easy, and working with different communication styles. One of my tendencies that I've noticed and I see this a lot on ADHD support forums, so I think it's a common pattern for ADHDers - is that when something starts to get a bit tricky, I tend to catastrophise, build it up into this huge thing in my head and get convinced that everything is an unfixable disaster and I may as well quit now. However, the other thing I've learnt about myself is that when I experience this and there's a short delay on me being able to bail out, like if I'm completely failing at getting DC to sleep and I text DH and he says "I can come in in 15 mins" 9/10 the issues all resolve within that short delay period and I can actually handle whatever it is after all.
So it made me think maybe I just experience that kind of feeling when it's all about to get better anyway. And then as an experiment I decided that I'd try giving myself a short deadline in the future by which time, if things aren't getting any better, I can still quit no guilt attached. For something like this job, I'd probably give it 2 weeks if you need to give notice, or 4 weeks/1 month if you can quit with no notice. It seems to help, because first of all I am not stressing so much about it because I know that it ultimately doesn't matter as I'm going to quit anyway. But secondly, it just gives teething issues a bit of time to settle in and let me adjust to the transition.
To respond to some of the things you said about this place specifically:
I couldn't handle how everyone did things differently over the smallest of tasks.
IME this likely means that it doesn't really matter how the task is done or that the systems about who decides what is done when and how just aren't especially stable, or other people maybe don't know what they're doing either. I would try not to get hung up on this, and I think I would see it as a sort of challenge. When there's a new person there, be a bit more reticent and check with them what they feel to be the way to do things. Or if they do something different, ask them questions about it. Or if they ask you questions, say "Oh this is how Sandra showed me last week, is that right?" Or if you can't remember how to do it you could say something like "Sorry I'm new and I've been on 50 different jobs here - show me how we do this again?" or "Is there a set way to do this?"
There is so much to learn and do...I am going from one task to another, without mastering the basics for one thing.
It's a bit tricky to give advice with this without knowing the context of what kind of work it is. But I suspect that this is one of the things which will get easier in a fairly short time because eventually you will rotate through everything and come back to something which is familiar again. It can be an overwhelming and stressful way to get into a new workplace or team. Although if you can put less pressure on yourself to master everything, and accept that everyone doing things differently is probably a sign that it's always been a bit like this, I think the variety in a way could be quite fun? Though I can see it would be stressful esp if there is a query over ASD as a lot of autistic people find it very difficult not knowing what to expect. It might be worth calling or emailing the day before to see if you can get an idea of what you'll be doing the following day, as it's possible they have it planned out by then.
I also think that it might be that by moving around different tasks and roles you'll end up learning more parts which add up into the big picture of the organisation and how it works, and from that you get more of a sense of the overall process, as well as being flexible to fill any role depending on what needs doing at various times.
Sometimes ND can make it harder to piece these things together, but OTOH I find for myself, it can be harder to get very much into one role when I don't understand where that sits inside the bigger picture. And I wonder whether this might be where you are stuck now, because each of these tasks feel disconnected and sort of pointless. So I might suggest approaching the next session as a sort of fact finding mission to try and see if you can make a link between whatever you are doing that day to what you have done previously. IME, once I understand this link, it also makes it easier to fill in any gaps of "What am I actually supposed to be doing here?"
I am now on the phones and I hate it. I want to be on reception but I am now shadowing half the day there because they want other volunteers to be on reception.
As a PP said it could be that reception is a popular role, so they are trying to give everyone a turn.
Phones are also a fairly universal difficulty for most people under about 40. I know there is this narrative that it is especially difficult for ND people and I do also hate making phone calls, but I did find when I have worked jobs where the person handed me a phone and said "You need to call this person and say this thing" that once I did it it got easier. If there are genuine difficulties e.g. you're getting so panicked you can't speak or struggling with the technical systems or whatever then it might be different, but my gut instinct is to say give it a good shot even if it's not your favourite job. It might be that you get moved on to something else after a short time anyway.
ALSO:
I think it's perfectly OK if you decide to say to the coordinator that the work is not what you expected, and actually you are willing to do XYZ role but not ABC. Or even you are only willing to stay for reception work and you won't do anything else. However I think you do need to accept that they may well say you can't pick and choose, in which case you should say then thanks, but this isn't for me. It is perfectly fine to set this boundary (what roles you're willing to do/not do) and it's also OK for them to say actually, our volunteers do ABC and XYZ. Use it as a practice to overcome the people-pleasing reflex to agree to ABC if you have made this decision, because it honestly does not matter to them and will not offend or disadvantage them if you ultimately decide to stop volunteering. Volunteers come and go all the time.