This was why the Jews were seeking all the more to kill him, because not only was he breaking the Sabbath, but he was even calling God his own Father, making himself equal with God.—John 5:18
Okay, so the biggest problem with the quasi-evangelicals justifying their referring to God as "Mother" is not necessarily their feminist ideology or their misapplying actual biblical metaphors (like Matthew 23:37, for instance). Those are serious problems of course, but the real trouble lies in the very area in which they claim continuity with orthodoxy—discipleship to Christ.
What I mean is, it's becoming more and more common for these folks who see nothing wrong with calling God "Mom" say that their faith is less about doctrinal truth claims and more about "following in the way of Jesus" (or whatever), but what they seem to miss (or ignore) is that "the way of Jesus" was to relate to God as Father. Yes, God is spirit and therefore without gender, but the Son of God exclusively referred to the first person of the Trinity as "Father." And that is the way he taught his followers to relate to God (Matt. 6:9, etc.).
The progressive evangeliwhatchamacalits seem to think they can mess with the revelation of the nature of our relational God without messing with the revelation of the nature of his Son. But we find all our information about "the way of Christ" in the same Bible we find all our information about God our Father. To mess with God as Father, then, is also to mess with Jesus as Son. (Unless one wants to argue that the eternal Word of God, the second Person of the Trinity, is not God's eternally begotten Son but only became "Son" when he incarnated male flesh.)
That God is genderless is besides the point, really. He has revealed his relational nature to us in the first case as Father and in the second as Son. That was his call, and it's no more a suggestion than Jesus' command to love our enemies. If you want to mess with the biblical revelation of God's Fatherhood, then, you end up messing with the revelation of Jesus Christ himself, like "red letter Christians" with bottles of white-out. Might as well call Jesus "daughter," I s'pose.
For to which of the angels did God ever say, "You are my Son, today I have begotten you"?—Hebrews 1:5
But the hour is coming, and is now here, when the true worshipers will worship the Father in spirit and truth, for the Father is seeking such people to worship him.—John 4:23