Circa 1495, would a baron have worn the livery of the Earl of his Palatinate county? For example, would Thomas Butler, Lord of Warrington, have been insulted if Thomas, the earl of Derby asked him to wear his livery for Henry VII's visit? Butler had his own retainers and his own coat of arms, so I am assuming that his retainers wore his badge and livery? Any help is appreciated.
No baron would ever wear the livery of another.
Livery originated in Europe in the 14th century and was applied within the household and by followers of the noble they owed fealty to.
A baron would have his own coat of arms and his retainers would wear his colours, his livery.
Likewise for an earl, although he would likely (not always!) have more retainers.
No noble would ask another to wear his livery. That would go against all that the feudal system stood for.
The clothes you wear are your identity, and there even were laws to forbid you to wear clothing other than what you are. Merchants could not clothe themselves better than nobility, despite being richer. Some colours and materials were restricted to royalty. It was taken very seriously indeed.