In this work, we solve the fluid-structure interaction (FSI) problem with the Isogeometric Divergence-Conforming Immersed Boundary Method (IDCIBM) [1,2], where we include the Navier-Stokes equations for the description of the fluid motion and the constitutive equations of a Neo-Hookean material for the solid phase. In the IDCIBM the Eulerian velocity-pressure pair is discretized using divergence-conforming B-splines, which leads to inf-sup stable, H1-conforming, and pointwise divergence-free Eulerian solutions. Different setups are solved to show all the above-mentioned properties of the DCIB method together with mesh-independence studies, comparisons with other methods from the literature, and measurement of convergence rates. The DCIB method leads to completely negligible incompressibility errors at the Eulerian level and various orders of magnitude of increased accuracy at the Lagrangian level compared to other IB methods. The method has been extended to handle non-contact interacting deformable solids controlling, when necessary, the interactions between particles with the software package ESPResSo, taking advantage of its wide variety of already implemented short and long-range interacting forces. This numerical approach allows us to simulate problems in the fields of elastohydrodynamics, immersed polymer brushes under fluid flows or microswimmers made of interacting deformable particles with no restriction on the separation distance.