You can be pro-choice and be a conservative. The divisions between conservative, progressive, etc. are not well-defined, strong boundaries but ideologies. In general if you profess a majority of political opinions that are opposed to your country's/locale's conservative policies then it might be hard for you to justify it. But there are pro-choice American Republicans. There are pro-LGBT American Republicans. There are even pro-democracy American Republicans (a shocker, I know).

But I'm contending that American Libertarians (as in the party, not the very vague ideological notion) are Conservatives and very close to American Republicans. They share, in effect if not in stated policy, the same stances as Republicans based on their support for bills and politicians. They are essentially just a slight white-washed versions of Republicans.