Yes under Mao, but after Deng came to power the family regained significant political power.
Xi's father Xi Zhongxun was one of the Eight Elders [0] during the Deng era, and supported the Tiannamen crackdown. He was the Chairman of the Internal and Judicial Affairs Committee until 1993, and while the Chairman of the NPCSC (Wan Li) was in the US during the crackdown. He was also in charge of Guangdong after the Gang of Four were purged [1] and was the party leader who created what became the Shenzhen SEZ. And Xi Jinping's early mentor Geng Biao was the general who purged the Gang of Four [2] and worked with the US to modernize China's military capabilities [3].
The Geng Biao connection is a major reason why PLA Modernization is such a personal ambition of Xi's today - it was what gave him a major leg up in his career, and allowed him to differentiate himself from other Princelings and the Youth League cadre during his climb up the party ladder as well as during the succession showdown against Bo Xilai.
[0] - https://www.scmp.com/article/662093/eight-immortals-who-jock...
[1] - https://www.lemonde.fr/en/international/article/2025/07/16/x...
[2] - https://www3.nd.edu/~pmoody/Text%20Pages%20-%20Peter%20Moody...
[3] - https://history.state.gov/historicaldocuments/frus1977-80v13...