We develop a theory of a resonant effect in protein-membrane coupling taking place in the vicinity of instabilities in tubular lipid membranes (TLMs) under longitudinal force and pressure difference constraints. Two critical low-energy modes defining the stability domain boundaries are found. We show that these modes mediate long-range TLM-protein coupling and interactions between absorbed proteins. Besides, TLM mechanical instabilities strongly influence protein desorption and protein cluster nucleation on TLMs. Model predictions can be tested over a large spectrum of mechanochemical conditions.