Does the failure of Muslims in the West to disavow those who adopt Western culture - such as same-sex marriage and artificial insemination outside of marriage - while claiming to be Muslim, prevent them from entering Paradise?

A Muslim does not commit disbelief by failing to boycott someone who deserves to be boycotted. And whoever dies upon Islam will enter Paradise, even if they fell short in some obligatory or supererogatory acts. A servant is only deprived of entering Paradise by committing shirk (associating partners with Allah), as Allah Almighty says: "Indeed, he who associates others with Allah - Allah has forbidden him Paradise, and his refuge is the Fire. And for the wrongdoers there are no helpers."