Is it in harmony with the Scriptures for a woman to be a preacher or an elder in the church of our Lord?
It might not be politically correct, but the answer is "No." In fact, the Bible specifically condemns the practice of women serving in this capacity.
In Paul's first letter to Timothy, we read, "Therefore I desire that the men pray everywhere, lifting up holy hands, without wrath and doubting: in like manner also, that the women adorn themselves in modest apparel, with propriety and moderation, not with braided hair or gold or pearls or costly clothing, but, which is proper for women professing godliness, with good works. Let a woman learn in silence with all submission. And I do not permit a woman to teach or to have authority over a man, but to be in silence. For Adam was formed first, then Eve. And Adam was not deceived, but the woman being deceived, fell into transgression. Nevertheless she will be saved in childbearing if they continue in faith, love, and holiness, with self-control" (1 Tim. 2:11-15). This passage not only prohibits women from "teaching" or "having authority over a man," but it also gives us the reason: "For Adam was formed first, then Eve...But the woman being deceived, fell into transgression."
After reading this passage some women might wonder what role God has for them. Paul explains that the godly women "will be saved in childbearing." Paul is saying that women are to find their salvation by fulfilling the role God gave them, i.e., bearing children and guiding the home. I know of no greater work that women could do than to bear children and instruct them in the knowledge of God.
In 1 Cor. 14, Paul discusses the matter of spiritual gifts in the first century church. After instructing the church that those who speak in tongues had to "keep silent" if there was no interpreter, and that one prophet had to "keep silent" if another prophet was speaking, he says, "Let your women keep silent in the churches, for they are not permitted to speak; but they are to be submissive, as the law also says. And if they want to learn something, let them ask their own husbands at home; for it is shameful for women to speak in church" (1 Cor. 14:34,35). To this passage is attached the following admonition, "If anyone thinks himself to be a prophet or spiritual, let him acknowledge that the things which I write to you are the commandments of the Lord" (1 Cor. 14:37).
Brother David Lipscomb made this observation on Paul's instructions to the church at Corinth: "No instruction in the New Testament is more positive than this; it is positive, explicit, and universal; and however plausible may be the reasons which are urged for disregarding it, and for suffering women to take an active part in conducting public worship, yet the authority of the inspired apostles remains positive and his meaning cannot be misunderstood. He looks at it from every viewpoint, forbids it altogether, and shows that from every consideration it was to be regarded as improper for them to take any active part in conducting the public service." (Commentary on First Corinthians, p. 216).
Beyond this, in the qualifications given for "bishops" (i.e. pastors, elders, shepherds), Paul twice says they must be "the husband of one wife" (1 Tim. 3:2; Titus 1:6). Unless you are willing to accept two lesbians living together and call it a "marriage," and one of them be considered as the husband, there is no way for a woman to be "the husband of one wife."