Inteins are autocatalytic protein domains that post-translationally excise from protein precursors and ligate their flanking regions with a peptide bond, in a process called protein splicing. Intein-containing DNA polymerases of cyanobacteria and nanoarchaea are naturally split into two separate genes at their intein domain. Such naturally occurring split inteins rapidly self-associate and reconstitute protein-splicing activity in trans. Here, we analyze the in vitro protein-splicing activity of three naturally split inteins from diverse cyanobacteria: Oscillatoria limnetica, Thermosynechococcus vulcanus, and Nostoc sp. PCC7120. N- and C-terminal halves of these split inteins were mixed in nine combinations, resulting in three endogenous (wild-type) and six exogenous combinations. Protein splicing was detected in all split-intein combinations, despite a 30-50% sequence variation between the homologous proteins. Splicing activity proceeded under a variety of conditions, including the presence of denaturants and reductants and high temperature, ionic strength, and viscosity. Still, in a high concentration of salt (2 M) or urea (6 M), specific combinations spliced significantly better than others. Additionally, copper ions were found to inhibit trans splicing in a reversible double-lock reaction. Our comparative analysis of naturally split inteins in endogenous and exogenous combinations demonstrates the modularity of trans protein-splicing elements and their robust activity. It suggests tight interactions between split-intein halves and conditions for modifying the specificity of intein parts. These results promote the biotechnological use of split inteins for controlled assembly of protein fragments either in vivo or in vitro and under moderate or extreme conditions.