You don't say how old your DC are OP. I think that's key to whether this is really their decision, or yours.
Most likely, you have offered information selectively, leading them to a pre-approved conclusion, which they may not be old enough, or accomplished enough at independent thinking and research, to challenge effectively. Isn't that what most of us do with our DC, about most things, most of the time? Feed them our own views, sometimes caveated around with a summary and dismissal of other options?
My question would be why it is important to you that they display your choice at school and attempt to deal with the complexity of the issue and reconcile the difference between your view and the school's approach there, in public, rather than doing that at home? Some DC relish debate, investigation, or just being different or contrary, others feel very awkward about being singled out and different. So I think the most important question here concerns the personalities of your children.
Poppy symbolism is complicated. It is not simple. It is contested. It is often politically loaded and frequently appropriated.
People who judge or lambast anyone for making the free choice not to wear a red poppy, or to adopt the white poppy instead, are acting against the tenets of the 'freedom' they claim the remembered soldiers died for.
There is a lot to discover, a lot to digest and many reasons why people, including former soldiers, choose not to wear red poppies. A quick read of the wikipedia page on Remembrance poppies gives a superficial sense of this. Further reading offers deeper understanding. e.g. The late Robert Fisk's columns in the Independent, about why his WWI veteran father abandoned the poppy and he followed through respect, were interesting (to start with, if increasingly polemical and overwrought as time went on). They offer a glimpse of one reason, anyway.