Firstly, there is nothing wrong with 4 year olds being taught this. It happened and it’s history.
Secondly I understand and sympathise about the anxiety. My DD is an extreme over thinker and was diagnosed with anxiety at a young age. We still let her learn about everything at school and dealt with any worries.
We found (and I think a previous poster suggested similar) that reassurance alone didn’t work. We had to help her talk and think through her thoughts (even at 4 years old) and then correct/support her assumptions. At an age appropriate age.
So at 4 years old “what do you think they meant by red” “Do you know about poppies meaning remembrance” “what would a field of poppies look like” etc
Then “why do you think the soldiers died” “they wanted to protect their families and families like us many years later. Wasn’t that nice and kind of them. They must have been very nice people” “ maybe they are still watching over us now to make sure we stay safe (if he thinks they are still around in spirits form). Shall we say thank you to them”
We tried to do that straight after school so there was a gap between talking about it and bedtime
We also found a worry doll (that she could tell her worries to) helped and a brave bear (build a bear with a recording that said something like “ I am here to look after you and I love you. We can be brave together”) was something she could cuddle back to sleep. We also put a dream catcher up and told her it would try to stop her bad dreams.
We also tried to talk about something positive just before bedtime. Things like where would you like to go on holiday? What would you like to do in the summer holiday? Shall we go shopping tomorrow and you can choose a treat” etc helped focus the dreams on something positive instead
Shes a teenager now and still has anxiety but it’s completely manageable now and nothing like it was when she was 4-6 years old