YANBU, not at all... other than having an app like this on your personal devices if that's the case.
I'm a teacher, so is DP and we have school-aged DC of our own. I do not have my school email or other apps on my phone and only have them on the device provided by school. The school messaging app is set up so the school can send messages out but parents cannot reply. They tend to call the school office with moans etc. rather than email, even though they can access our email addresses easily. The school website explains we are teaching between 9am and 3.30pm and asks for parents to be aware of this when emailing, saying we'll respond within a few days.
Does your school have a comprehensive website @Elendel? In your situation, I would delete the app from any personal devices and try to find a way of setting up an auto reply. I would put a lot of effort into making it detailed. If it's not possible to autoreply, I'd prepare a stock response that is pasted to every message received. It would read something like this...
Thank you for contacting me. I'm teaching until 4.30pm today so may not have a chance to read your message until after that. If you are the parent of a child in 7E, please read through the Q&A I've put together to help you work out who your query should be directed to.
Q. My child is going to be off school/needs to leave early for an appointment.
A. Please contact the school office about this.
Q. My child has lost an item or left something somewhere.
A. If your child knows where they last year the item, they will need to go and check that place themselves, making sure they speak to the adult who teaches in that space. The lost property is stored in XX, please get your child to look in there every lunch time for the next week or so in case it turns up
Q My child hasn't done their homework
A. Please ask your child to speak to the teacher who set the work
Q My child has been given an unfair consequence.
A Please ask your child to speak to the person who gave them the consequence
Q. Why is my child marked absent for a lesson they were definitely at?
A. Please ask your child to speak to the teacher whose lesson it was.
Q My child's goldfish died last night and they're feeling sad so I'd like all the teachers to be aware
A. Sorry to hear this. Please email the main office and ask them to let your child's teachers know.
Q What does my child have to wear for yoga lessons?
A. Please go to the uniform and PE kit page of the school website. Further questions about PE kit should be sent to the head of Physical Manoeuvres. General uniform queries should go to the main office.
If you are the parent of a student I teach geography to and you are messaging about the subject, please look on the department's curriculum page of the school website to find out what your child is learning about, the exam syllabus and handy revision resources.
Most of the queries I receive are requests for information that can be found on the website so please do spend some time exploring it. Mrs X, Mr Y and Ms Z are in the school office during teaching hours and will be able to help you with most things so do give them a call. Please be assured that I do read the messages I receive but I am usually only able to respond to messages about my own geography classes or 7E form time. If I haven't replied to you within 2 teaching days it is because your query is not specific to me and needs to be dealt with by someone else. Do ask the school office if you need help working out the best person to send your query to.
Best wishes,
@Elendel
If I ever contact my own DCs' teachers I try to remember to schedule the email to go at 8am rather than on the evening I've written it. I also try to make it clear if I'm just passing on information and do not need a response e.g. I wasn't sure who needed the info or it's something my DC can be given a response to in the next lesson.