In the US the "right wing" is not a monolith, in fact is more from an ideological stand point the right today is more diverse in political opinions than the lef

In the US the "right wing" is not a monolith, in fact is more from an ideological stand point the right today is more diverse in political opinions than the left, as the left has cast out many of their more moderate members (i.e the Blue Dogs) Conservatives do not really hold you own your body, conservatives tend to believe in various types of religion which puts your body subservient to a higher power or god. Thus is immoral to kill yourself. It is not a property rights argument, it is an ethical argument., then you have the libertarian right, which do use property rights and self ownership and many support assisted suicided, the ones that do not oppose governmental assisted largely because what is being perceived to be playing out out in real time (rightly or not) from Canada whereby the state has an incentive to direct people to suicided and maybe even force / Coerce them to "voluntary" dying either as a goal of the program, or just agents of the state abusing their positions. In either case state level suicided is seen as huge opening for abuse where even if you think people have the right to end their own life, trusting government with that power is not something they want to support.