to my understanding, that is very much not true.

the terminology of being a "conservative" did not come from supporting conservation of nature. that might be one aspect, and indeed, still today, there are conservatives that are very much interested in the conservation of nature, but this is not where it came from. it came from schools of thought in the american and french revolution concerning conservation of aspects of tradition, aristocracy, royalty, and religion.

afaik, this has also been the case tbroughout american history as well. perhaps you are referring to people like teddy roosevelt, who identified as a conservative to the public and had conservationist views and policies.