As Stephen remembers Kevin Egan talking about his Irish nationalist aspirations, he recalls a coinage from Shakespeare's Henry V: "To yoke me as his yokefellow, our crimes our common cause." The allusion indicates that Stephen has no interest in becoming an apprentice revolutionary.
In act 2 scene 2 of Shakespeare's play, the King and his nobles prepare to embark for war in France, after sending three English traitors off to face the executioner. The next scene shows three of Falstaff's lowlife companions, Bardolph, Nym, and Pistol, preparing to join the expedition. Their motives are anything but noble, and the way their number mirrors that of the aristocratic conspirators suggests that Henry here faces another kind of internal threat. Pistol, the vainglorious pugilist of the trio, makes clear that their chief interest is in pillaging:
Yoke-fellows in arms,
Let us to France, like horse-leeches, my boys,
To suck, to suck, the very blood to suck! (2.3.54-56)
As the campaign unfolds, Bardolph is caught stealing from a French church and King Henry, who has explicitly forbidden such looting, sentences his old drinking buddy to be hanged: "We would have all such offenders so cut off" (3.6.107-8).
Kevin Egan is an Irish fighter living in France, spouting militarist rhetoric. By thinking of him as a "yokefellow" looking to yoke others into his cause, Stephen makes clear that he wants no part of the aging fenian's program of violent "crimes."