Shane began his USL Championship career in 2019, signing with Loudoun United in mid-August. In that debut season, Wiedt played and started seven matches, and he picked up his first professional point with an assist in the final match of the season against New York Red Bulls II. The club signed him to an extension for the 2020 season, and the defender played fifteen matches for the Eastern Conference side. He scored his first professional goal on August 23rd against Hartford Athletic.
Prior to the 2021 season, Loudoun did not extend Wiedt’s contract, leading the defender to sign with Pittsburgh Riverhounds SC in late April. Wiedt played 32 games for Riverhounds in the 2021 season, starting in 29 of them. His defensive performance in those matches helped lead the Pittsburgh side to eleven clean sheets. Shane would return to the Riverhounds for the 2022 season, put up similar numbers, starting in 30 of 35 matches played, and helped the Riverhounds to ten clean sheets.
After leaving Riverhounds after the 2022 season, Wiedt joined Sacramento Republic FC, where he has spent the past two seasons. In the 2023 season, Shane started 33 of 34 matches, accumulating 2,849 minutes. He also led the team in interceptions with 44. Wiedt suffered a broken clavicle in August 2024, limiting his participation to 16 matches this past season.