To think they should let her take part?

Fantastic news OP! Some of the comments here are ableist and discriminationatory under the guise of being 'caring' and making adjustments (that you and your DD did not ask for).
Also, any pupil could have a meltdown or find the role overwhelming, not just those that are ND. Every pupil should have the same opportunities to participate.

As a side note, every secondary school I visited had people - students and teachers - specifically in the library.

Visiting families were stopping for some time and asking lots of questions.

No one seemed miffed to have been allocated "the library".

They've probably put her in the library for one of two reasons. One is that they think she might be particularly helpful there. The other is that they're worried she might not cope with the general showing around (they were perhaps surprised that she volunteered). If she couldn't go on a trip without an LSA, it's possible they think there should be one on hand, and she can't really have one trailing round with her on the tour.

I think there are two approaches you could take. One is to contact the HoY and say "she was actually really keen to do the showing round, and I think she can do it - she's really disappointed you've allocated her to the library and thinks you don't think she can - I wonder whether a swap is possible" (or you could ask the learning mentor to do this). The other is to to say to your daughter that they probably think she'd be particularly good in the library, and she'll get to meet all the parents, and help her think about what she might say. She could be pro-active: "Hello Millie, do you want to take a couple of minutes off while I tell your guests about the library."

I think if I was the HoY I'd look to see whether any of those coming to the open day have ASD, and perhaps get her to take them round. Even without disclosing anything, the parents may deduce, and would probably understand if she struggled with the task - and be pleased to see that she was given the chance.

When I was in y7 the library was my favourite place! There were loads of interesting books on stuff like fashion and makeup that I didn't have access to at home. There were computers there and you could do mocked up newspapers and write articles and they had microfiche! This was the late 80s. Lol
I would have been really happy to be in charge of the library tour. Most of the rest of the school is probably just boring classrooms, many of which your daughter might not even have used or visited herself yet.
Could she do some research about a topic she likes and incorporate that into the tour, I found these things here and here and I made this on the computer over here etc.
I'd try and make the most of the opportunity. It could be great for her and her confidence. Can she work with another friend with SEN (or not of course) if they do it in pairs?

I’m very surprised she wasn’t allowed on the trip because of her SEN, however it wouldn’t have been the HOY decision, that would have been higher up. As teachers we have no control over who the LSAs go to support (SEN lead) and if there are exams happening that does priority.

You've said yourself DD was anxious and you talked it through. Maybe school see a different DD, one who is still anxious and they are trying to support and include her.

Encourage her to do the open evening and by September it'll be a new HOY.

This isn't the hill to die on especially when you have another complaint about the trip.

I dont think they are excluding her. I think they are making adjustments to include her. if she was able to do everything a NT student could do, she wouldn't have ASD would she

If you were a parent attending an open day and one of the pair of students showing you around was silent or had a meltdown what impression would that give you of the school?

I think they are trying to do what is best for your daughter and the school.

If all they're doing is sticking her in the library without any responsibility that's extremely unfair.

Initially, I thought that the 'why' of what they were doing wasn't wrong although the 'how' was. Your statements somewhat contradict themselves , if your daughter would be really good at the role why does she need a confident partner? No matter how confident they're still a child and shouldn't bear any responsibility for your daughter being able to pull her weight.

However as @itwontletmechoose points out they could re-organise the roles to give your daughter something suitable but important.I f they had enough kids, they could also have teams of twos AND threes. Your daughter could be in one of the latter.

They need to give some real thought to this.

I'm a teacher and at my school open evening my mum came round with my DC just to see it... They were toured round by a lovely student with ASD. She had a complete meltdown, her partner in the tour fell apart with worry, and my mum brought them both to me as she could (thankfully) remember the way. The poor student was beside herself with concern about 'letting people down'.

She spent the rest of her time at the school coming back to my room from time to time to ask about my DM and DC and how they were.

I'm not saying this is what would happen for your DC, but just that prior experience may have made them err on the side of caution with this.

It's a very public facing role to have a go at.

I think they should have been more of a conversation with you and your DD about what the options may be. And I don't think it should ever be one child separate from the rest for something like this. They could have easily created different 'teams' of children to work in different areas.

I'm torn on this one OP! ND myself.
She shouldn't have been excluded from the school trip.
However - showing people around with the accompanying unpredictable questions can be difficult for an anxious child. They're in pairs for a reason - it's very unfair on her partner if your daughter clams up. Equally, any other adjustment like having 3 instead of 2 is just going to mark her out as different and potentially be very awkward if she just trails along behind them.

It's extremely poor of them to not have followed up and explained this properly to you. And their reply is very dismissive. but I think having her in the library is a good idea. I wouldn't expect her to be gushing about their SEN provision after all this 🙄 but she can talk to other SEN parents and their kids about her experience! Also , if she gets overwhelmed, she can quietly retreat.

I'd push them for more structure and bigging up of her role personally, not just 'showing people around the library' as opposed to doing exactly as the other children. Maybe even have another child there with her so it's just not her and the SEN team.

I actually think that your dd could be very valuable in the library. When we looked round my DD’s secondary school she was really really happy to discover that she could come to the library at lunchtimes whenever she liked and just sit in silence and read a book.

It was nice having that explained by the librarian but to have a Year 7 tell her about it would have been better. Especially if it is one that she recognised as a bit of a “twin soul”. (Dd is neurotypical but she is definitely “quirky”.)

The children of the parents who are taking to the LSA about SEN provision will value input from your dd.

Fight it in the background, especially as there are several issues, but try and spin it as a positive to your DD. She's familiar with the library, she can parents'/children's minds at ease that there is a quiet place available and what she likes about it etc.

As an aside, will the LSAs be in there specifically for your DD or for another reason? Seems odd to restrict several staff to one room .