The problem with supersessionism isn't so much its attitude towards Judaism as an ethnoreligion as it is the advancement of a narrative about Christian origins that verges on treating the faith ahistorically, but I get that that's not really the point so I'll shut up about it.
Actually that's something I'm a bit intrigued about, seeing as how it's difficult to square a complete rejection of supersessionism with much of the New Testament, as it's made clear most of the first Christians were Jewish converts and Paul's writings on the Mosaic Law. Unless you want to argue that Jewish converts were only OK for a period of time, but that's something that I have a tough time backing up.The problem with treating the way in which Christianity succeeds the Old Testament law as supersessionism over something comparable to or existing in continuum with modern rabbinic Judaism is that modern rabbinic Judaism can be shown to have developed out of the same environment as early Christianity in somewhat similar ways. Judaism as we know it
isn't what got superseded; it's a sister religion more than a mother. Treating it otherwise ignores both the actual nature of the religious culture in which Christianity arose and the existence of history and historical development within Judaism.
I'm not even thinking of this as relevant to the subject of evangelism and I have a tough time articulating my understanding of why you might be.