This even went so far that certain Bible translations chose gender-neutral language over accuracy. This, in turn, became part of many Masses. Here is an example:
Romans 12: 6-8 New International Version
Original
We have different gifts, according to the grace given us. If a man's gift is prophesying, let him use it in proportion to his faith. If it is serving, let him serve; if it is teaching, let him teach; if it is encouraging, let him encourage; if it is contributing to the needs of others, let him give generously; if it is leadership, let him govern diligently; if it is showing mercy, let him do it cheerfully.
New Translation (gender-neutral/inclusive)
We have different gifts, according to the grace given to each of us. If your gift is prophesying, then prophesy in accordance with your faith; if it is serving, then serve; if it is teaching, then teach; if it is to encourage, then give encouragement; if it is giving, then give generously; if it is to lead, do it diligently; if it is to show mercy, do it cheerfully.
Certain techniques are used to change a text from gender-specific to gender-inclusive: using "you" instead of "he" when referring to God, removing gender-specific words like "Lord", replacing "he" with "God" each time, etc.
There are many problems with this:
1) Bible as Word of God
The Bible is the Word of God, and therefore cannot be changed. There are several strong warnings about doing this in the Bible itself. The goal of translators is not to render the Bible politically correct but to render it accurate. We cannot say God made a mistake. Also, claiming the Bible to be sexist, would be tantamount to calling God sexist, unless you stop believing in the inerrancy of the Scriptures.
2) God reveals himself as a father
God is constantly referred to as "Father" in the Bible, by none other than Jesus himself. By refusing to acknowledge this, we are contradicting Jesus. Consider the Lord's Prayer, "Our Father, who art in heaven"
3) Jesus took on the form of a man at the incarnation
Not as a woman or non-gendered entity. Jesus is a man, therefore it is appropriate to refer to him as such.
4) The priesthood
A related point is the priesthood. A priest shares in the priesthood of Jesus Christ, and Christ's maleness is essential to his character, his being. The priest proclaims "this is my body" and at this moment, he is speaking In Persona Christi. He's not just repeating the word's of Christ, but acting in the person of Christ. Christ's maleness is essential to his identity, and therefore the priest who becomes an "alter Christus" must also be male.
5) God has always been referred to as "he"
God is masculine in monotheistic religions, even though many polytheistic and pantheistic religions existed at the time of the Jews and early Christians, which had multiple gods, some of whom they called "she". Jesus could have easily taught that God is feminine or "Mother", but he did not, and this was never the understanding of the Jews. But why? God is masculine, the universe is feminine. The reason is that God sends his grace from outside into the world, just as the male impregnates the female from without. A similar concept is found in the Church. Christ is the bridegroom, and the Church is the bride. Jesus sanctifies and leads the Church as the head, and we receive those graces. Jesus is the head of Church, just as husbands are the heads of the family, and the Church is the Body of Christ.
Peter Kreeft has produced a masterful essay on this topic, which goes into much more depth than my brief overview of the subject here. I suggest you check it out here: Sexual Symbolism
I think ultimately this whole issue once again comes down to obedience. Most of the time, women who advocate for calling God she, it, or a non-specific gender are also advocates for priestesses. Again, please check out Kreeft's essay on this to go more in depth. This article is not on female ordination, but it is important to note that Jesus selected only 12 men, no women. Since that time, only men have been ordained. It belongs to the ordinary Magesterium of the Church and is unchangeable.
On a personal note, I have been duped into this form of gender-inclusivism in my own experience. In the part of the Mass known as the Preface, the following is said:
Priest: The Lord be with you.
People: And also with you.
Priest: Lift up your hearts.
People: We lift them up to the Lord.
Priest: Let us give thanks to the Lord, our God.
People: It is right to give him thanks and praise.
I have been accustomed to saying "It is right to give God thanks and praise". I notice now that saying "God" the second time is unusually grammatically. It would be like saying "There's Joe. Joe is walking over here. I hope Joe has the movie." Instead of saying Joe again, you would probably say he." I guess I got used to it after hearing many others using this. At one time the bishop asked me what follows "Let us give thanks to the Lord, our God." and even then I repeated God. It is clearly spelled out in the liturgy to say "he", rather than "God" in this instance.
This, of course, is a minor thing, but the bigger issue is that of disobedience and radial feminism which causes inaccuracy of translations and hostility toward the nature of God.