Different kinds of Lutherans regard the reception of Communion differently. I grew up Missouri-Synod Lutheran, very conservative. Only LCMS Lutherans can take communion in their churches. I changed to the Evangelical Lutheran Church in America, one which generally welcomes any baptized Christian to Communion. They also(gasp!) hold that women have an equal place with men in the church, something the LCMS doesn’t. Neither of these two denominations believes that the bread and wine actually become the flesh and blood of Christ(transubstantiation), but they both believe it’s more than a simple memorial, that Christ is “In, with and under” the elements(consubstantiation)
I am now Episcopalian(too long a story for here). In my congregation the priest generally says something like this “All who love God are welcome at the Lord’s Table,” or “this is not the Episcopalian’s table, but the Lord’s.” We of the Episcopal Church in the United States of America (ECUSA) try to be open and affirming. Just ask Gene Robinson.