The Lutheran Reformers rejected Transubstantiation (and consubstantiation), on the grounds that it tries to explain the mystery of the consecration in a metaphysical/ philosophical Aristotelian construct. Instead, we speak of the real presence in terms of Christ’s words: “This [bread] is my body”, etc. And we further rely on St. Paul’s usage of bread and wine/ body and blood in 1 Corinthians.
The Lutheran Reformers adopted Luther’s use of the term Sacramental Union, which in many ways, mirrors the Hypostatic union of Christ being fully man and fully God.
Lutherans wil say the true body and blood are received “in, with, and under” the bread and wine, though the term “with” should not be construed as anything other than “is”.
Christ takes the bread in His hands, and says the words, “This [bread] is my body”, etc.
And this is what we believe - the bread is His body, the wine is His blood.
Personally, I do not see Transubstantiation, as described by Catholics, as being a stumbling block, and see it as a reasonable expression of the truth of the mystery.
Jon