There are some ongoing physical changes, e.g. increase in average height
and decrease in jaw size, that show shifts since Jesus' day. We change our
environment to suit ourselves rather than adapting to it, so it seems as
though only something drastic would cause more significant mutation. The
problem of species definitions also arises here.
I don't think such physical shifts would affect our relationship with God.
Glenn Morton strongly argues that previous hominid species have also been
human in the sense of made in God's image; this would imply that future
species could be incorporated, too.
C.S. Lewis suggested that becoming a Christian could be viewed as the next
step in human evolution. Although I think he was thinking more
teleologically than is accepted in modern evolutionary thought, it is an
idea worth further examination, at least as a metaphor.