I think that the overall meaning of the poem is to stress Rumi's notion of spiritual evolution towards a universality of love. In the poem, there is a distinct moment that speaks to this reality:
A hand shifts our birdcages around/ Some are brought closer/ Some move apart./ Do not try to reason it out./ Be conscious of who draws you near and who not.
For Rumi, the poem is an exploration of this idea. In explaining the mutual dependence of organisms in the natural world, Rumi values this idea of placing emphasis and modeling ourselves after "who draws you." When Rumi introduces concepts and elements that move away from this, his contrast and purposefulness in bringing it out becomes relevant. As seen in the poem through religious allusions in Jesus, the balance between human beings and the natural world, the interdependence of creatures and humans with one another and with their own kind are all a part of this spiritual exploration in the poem. The poem is Rumi's Sufistic interpretation of the universality of oneness, a transcendent type of love that seeks to bring seemingly disparate forces together. For Rumi, the power or "force of friendship" is to provide a transcendent reason for being in a setting of contingency. Rumi points this out in the voice of the frog in the poem, a force that does not "conform to the laws of nature," but rather recognizes its own power in being. In Rumi's mind, the ending of the poem calls for human beings to discover this primal life force, embrace and cultivate it and do whatever is possible to nurture it when forces in the world seek to deaden it.