This is a school.
https://ico.org.uk/for-organisations/guide-to-the-general-da...
In the case of a permission slip - the school already holds lots of info that the school collects under the 'Public Task or 'Legal Obligation' bases.
The slip then contains additional information that is only collect because the kid is going on a trip, but is necessary for the trip. This would be collected under the Contract basis 'If you want to go on this trip, the following info is necessary'.
If the school also wants to take photos of the child on the trip, for example, then the parent will be asked for consent.
So to answer your question, the parent (assuming the child is under 16) could ask for:
1. The photo consent to be removed - in which case the trip must continue
2. The info pertaining to the school trip to be removed (in which case the kid would no longer be going on the trip)
But they cannot request the core data that the school holds to be removed, unless they take their kid to another school.
I work at a telco/ISP and GDPR training (and graded tests) is mandatory for everyone, from customer support to CEO.
It also coincides with FB's recent privacy breach news and overall general public dissatisfaction with FB's policies.
I know a lot of folks who simply don't use FB and are realizing that it's "really not free" in liability terms.
So does this turn into a groundswell? Probably not, I agree with you. However, it does put some fences up that is probably causing FB to feel a bit more nervous. GDPR may be the first of many such efforts...
Amongst "ordinary" people, there is a growing sense of unease about data collection - reflected in the "Facebook must be listening to my phone because they overheard a conversation I was having and now I'm seeing ads for it".
I believe people are starting to understand the implications of data collection and are quite unhappy about it.
In other words, are 99% of European citizens going to just click through what ever annoying prompts they have to in order to get to their facebook (thats what I would do) or is there an actual widespread cultural difference in the EU that would stop large segments from agreeing to this.