Originally Posted by joesch

Before and after can be beneficial given you know your bodies limitations.
Stretching like weight training both warm up and allow the body to work better, like warming up before you sprint or hill climb. They both need to worked gradually otherwise you may injure yourself by doing more than your body is use to.

Same applies to yoga and many other cross training routines.
When I started yoga many years/decades ago, I was still too competitive and pushed my body too far and caused injuries.

Bottom line, its good to add cross training routines, especially stretching, to your cycling but do so gradually based on your age and and current capabilities.