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The Law against ‘cross-dressing’ comes in the Law given by God to Israel through Moses at Sinai. It is recorded in Deuteronomy 22.
Deuteronomy 22:5 A woman shall not wear anything that pertains to a man, nor shall a man put on a woman’s garment, for all who do so are an abomination to the LORD your God.
God’s view is clearly stated. Christians are not under the Law of Moses, but God’s principles do not change. If we are baptised into Christ, we are to live a newness of life.
Romans 6:4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
We are to forsake our old way of life and be holy.
1 Peter 1:14-16 as obedient children, not conforming yourselves to the former lusts, as in your ignorance; but as He who called you is holy, you also be holy in all your conduct, because it is written, "Be holy, for I am holy.
It is incumbent upon Christians to dress ‘modestly’ - to wear clothing that does not bring disrepute on the name of Christ and does not cause offence. All that we do in our lives is to be done to the glory of God.
1 Corinthians 10:31 Therefore, whether you eat or drink, or whatever you do, do all to the glory of God.
Cross dressing seems to me to be a repudiation of our God-given gender and, if practised by a baptised believer, incompatible with a life in Christ. Those who persist in cross dressing will have no part in the kingdom of God.
I hope this helps.