Does touching the private parts during or after ghusl (for drying, moisturizing, or hair removal) invalidate wudu, and is this ruling specific to men, not women, or is the prohibited touching only that which is done with lust?

The opinions of scholars have varied regarding the issue of ablution being nullified by touching the private parts. The majority of scholars hold that it is nullified, citing Busrah’s Hadith: “Whoever touches his penis, let him perform ablution,” which indicates that touching the penis nullifies ablution, and this also includes touching a woman’s private parts. Meanwhile, Abu Hanifa and his companions hold that it is not nullified. Some scholars have reconciled between the narrations, restricting nullification to touching with desire, and interpreting the Hadith of non-nullification as referring to touching without desire. What the website prioritizes is the opinion of the majority due to the strength and authenticity of its evidence, and because Busrah’s Hadith is more authoritative than Talq’s Hadith due to the multitude and authenticity of its chains of transmission, and because Busrah narrated it in the homes of the Muhajirun and Ansar, who were numerous. A woman is like a man in this regard, due to the authentic Ahadith ordering her to perform ablution if she touches her private parts, such as the Hadith of Umm Habibah (may Allah be pleased with her): “Whoever touches his private parts, let him perform ablution,” which includes both male and female, and the term “farj” (private parts) includes both the front and back private parts of a man and a woman. This is also found in Musnad Ahmad from the Hadith of Amr ibn Shu'ayb, from his father, from his grandfather: “Any man who touches his private parts, let him perform ablution; and any woman who touches her private parts, let her perform ablution.” If a person follows a scholar who issues a different fatwa, there is no blame on him because the issue is one of ijtihad (independent reasoning). As for your mention that it is necessary to touch the private parts during or after ghusl, this is not the case. It is possible for a person to perform ghusl without touching his private parts after washing them at the beginning of his ghusl. And if that does happen, then ablution is nullified by it, and it must be repeated for prayer. As for repeating past prayers for which you did not perform ablution after touching your private parts, it is not obligatory for you, even if you were to adopt the opinion we prioritize in this matter.