The Bible distinguishes men and women, and each are given roles with respect to God and each other. So, that, in the first instance, may be the subject of the charge of sexism.
But, then, to anyone who accepts the Bible as the inspired word of God, how can they criticize God for what He has done and how He has revealed himself?
True, there may be some translations of the Bible that had some sexist language that was not present in the original text, and that should be corrected on general principles.
In Leviticus, there are prescribed longer periods of purification when a woman bears a female child as compared to bearing a male child. But, you have to go to reasoned exegesis of this and not jump to pre-ordained conclusions.
To charge the Church with being sexist demands specifics; it is too broad a subject to discuss.
The verses in Paul’s epistle about women being silent in the assembly are interesting. He advises that if a woman has a question, she should ask her husband about it at home. What a great way of encouraging communication between a husband and a wife, and what a responsibility for a woman to ensure that her husband “got” the message of the sermon. (there’s at least two ways of understanding the purpose of Paul’s directive.)