Supporting a right-wing coup against a democratically elected government should qualify you as a neoliberal.
Supporting coups against democratically elected governments is not at all "neoliberal": it is as antithetical to the ideology as it gets. Telling you this as a card-carrying Latin American neoliberal myself
It is a great achievement of neoliberalism that today every head of state in Latin America, bar Raul Castro, is duly elected, not imposed in a coup.
But Clinton never "supported" the Honduran coup. At worst, you can argue she tolerated it: a defensible position, given that the government that came to power did not intend to stay and conducted the election as soon as was practicable. Honduras is one of the most disfunctional countries in the region and the coup was an example of general incompetence, rather than some horrid devilish plot. It was not worth doing much about what happened, and nothing was done. But that hardly constitutes "support". To begin with, the interim government was never formally recognized and threat of non-recognition of the successor government was used to insist on reasonable conduct of elections. Hard to think of much more that could have been done: short of invading the country in order to reimpose Zelaya for the remaining 6 months of his term by force of US military. In fact, you might be unaware (since you do not ever talk to those people), but many (US) rightwingers at the time were accusing Clinton of exactly the opposite: betraying what they believed to be both a legitimate and a pro-American government, because of covert sympathies to the nasty leftist Zelaya "regime". Remember having those arguments myself: I was supporting Clinton in her
refusal to support the coup
So, I find the accusation of "supporting a right-wing coup" in this case to be, at best, only tenuously related to facts. At most, you could argue that more could have been done to oppose it - perhaps true, though I see little that could have been achieved that way. It is most definitely true that US played no role in organization or instigation of the coup (something that was purely Honduran from start to finish) and it expressed zero support or sympathy to its organizers. Accusing Clinton, as the Secretary of State at the time, of supporting that coup seems fairly disingeneous: if anything, there is ample record of the opposite.