I just read a short history of Liberia and it mentions Charles Taylor, with a throwaway line about him being 'possibly backed' by the USA. I am far from knowledgeable about the subject and would like to know whether or not the removal of Samuel Doe WAS approved of by elements of the Reagan/Bush administration during the first Civil War and, if so, why?
There is no hard evidence to this effect.
Interestingly enough, the Reagan and Bush I administrations were early supporters of the Samuel K. Doe regime. During the first half of the 1980s, Liberia received the greatest amount of US military and financial aid in all of sub-Saharan Africa and in total Doe officially received roughly $500m.
Charles Taylor was therefore obligated to find support elsewhere, which he received from the Gaddafi regime. Doe used this link to try and solicit help from the US, but in a twist of fate just as the civil war in Liberia began the Cold War ended, which meant that the US was no longer interested in sub-Saharan Africa. From that time onward the official policy of successive US administrations toward Liberia was non-interventionist and one of relative neutrality; the Bush I administration publicly maintained that there should be 'African solutions to African problems'.
The throwaway line you read may have been inspired by the long-circulated rumour in Liberia that Taylor received support from (and may have even worked for) the CIA. The Boston Globe published a story on this topic based on documents they obtained via a FOIA request, but issued a retraction shortly afterward.
Currently, there is no substantiated evidence that the US was responsible for the removal of Doe (or the support of Taylor). It seems unlikely, given the more general shift in foreign policy priorities within the State Department and as directed by the executive branch.