Vital functions of DNA, such as transcription and packaging, depend on the proper clustering of proteins on the double strand. The present study investigates how the interplay between DNA allostery and electrostatic interactions affects protein clustering. The statistical analysis of a simple but transparent computational model reveals two major consequences of this interplay. First, depending on the protein and salt concentration, protein filaments exhibit a bimodal DNA stiffening and softening behavior. Second, within a certain domain of the control parameters, electrostatic interactions can cause energetic frustration that forces proteins to assemble in rigid spiral configurations. Such spiral filaments might trigger both positive and negative supercoiling, which can ultimately promote gene compaction and regulate the promoter. It has been experimentally shown that bacterial histone-like proteins assemble in similar spiral patterns and/or exhibit the same bimodal behavior. The proposed model can, thus, provide computational insights into the physical mechanisms used by proteins to control the mechanical properties of the DNA.