First, precision is required when it comes to the issue of all doctrine as it is God's revelation of Himself to us. The Trinitarian nature of God is no exception despite the fact that we cannot fully comprehend that reality in all of its glory. To misunderstand what is revealed or to say we can conceive of the Father, Son, and Holy Spirit in ways more relevant or palatable to our culture is to change the very nature of God and thereby worship another God.
Second, the feminist influence in our culture, and indeed in evangelicalism, is clearly seen in the push to change patriarchal language with specific reference here to the way in which God has revealed Himself to us. We are not ignorant of the fact that God is Spirit (John 4), but He has indeed revealed Himself to us as Father, Son, and Holy Spirit. Further, when Christ appears, we will see Him as He is, the man Christ Jesus, who is also God. We will not see Him as her or as some androgynous hermaphrodite. Moreover, not only do we see a feminization of the church in the use of terms like Mother for God, but, even the construct of "Lover, Beloved, and Love" springs from the same well. Certainly God is love and for that we are grateful. But, while I used to tell my Dad before he died that I loved him, I certainly never referred to him as my lover, nor would any other real man for that matter.
Third, a discontentment permeates the church today in terms of the faith once for all delivered to the saints. That faith or body of truth, as saving, though certainly grounded in an experience with Christ, is nevertheless, in many ways, propositional. Experience oriented cultures are not content with the "normal Christian life" and always seek something extra. As noted, this same discontentment is expressed through a rejection of centuries-held orthodox understanding and language. Of course, inherent in such discontentment and in succumbing to feminist or other influences regarding doctrinal issues points to the larger issue of rejecting biblical authority which further relates to the work of God in the regenerate individual. The question arises, is He at work or not?
Fourth, to use the Trinity to support inclusivism is to misunderstand the nature of God in the unified purpose and efficacy of the economic Trinity. It is the Father who chooses a people for Himself from every nation, it is the Son who purchases that people off the slave block of sin through His blood, and it is the Spirit who applies the redemptive work of Christ to that people through the work of regeneration in connection with gospel proclamation. The thought that the Holy Spirit is at work in all lost people unto salvation apart from the proclamation of the gospel is not only unbiblical, but is destructive of missions motivation. But, the real issue here is what is implied in the thought that the Father chooses to save every single person and that the Son atoned for the sin of every single person. Such a construct produces a frustrated Trinity if the Holy Spirit does not regenerate every single lost person. To put it in plain terms, the Father and Son are moving the ball down the field with precision only to have the Spirit fumble it at the goal line.