  We describe algebraically, diagrammatically and in terms of weight vectors,
the restriction of tensor powers of the standard representation of quantum
$\mathfrak{sl}_2$ to a coideal subalgebra. We realise the category as module
category over the monoidal category of type $\pm1$ representations in terms of
string diagrams and via generators and relations. The idempotents projecting
onto the quantized eigenspaces are described as type $B/D$ analogues of
Jones--Wenzl projectors. As an application we introduce and give recursive
formulas for analogues of $\Theta$-networks.
