There’s evidence that Mudd ran a Confederate rat line for the Confederate Secret Service but none that he was part of the Lincoln conspiracy. Booth just knew the Mudd rat line existed and used it to get away. How much Mudd knew of Booth’s action is difficult to say. I don’t remember if he ever acknowledge knowing Booth before he was arrested. Surratt was probably railroaded. In her case it was likely revenge because Booth was not there to hang.
Read “Come Retribution & April 65 by William Tidwell” both on the Confederate Secret Service. “Come Retribution” focuses on the CSS & the Lincoln assassination, it hypothesizes that the Lincoln assassination was originally a CSS kidnapping OP gone bad. The original goal was to kidnap Lincoln to force a negotiated end & the release of Confederate POWs. The South collapsed before Booth could get the OP completely organized. Instead of standing down Booth went ahead and turned the kidnapping OP into a major assassination operation, basically a decapitation OP. SOS, VP & P were all targeted- only the P action worked.
Interesting...I was always interested in him as a physician, and his work in handling a Yellow Fever epidemic put him in good stead.