Why do conservatives make such a claim?
The worldview in the west that people take for granted today is the culmination of a perennial struggle between the spiritual (church) and temporal authority, (state) with the modern world today demonstrating the dominance of the temporal over the spiritual and now religion has been relegated to the private realm and completely divorced from any political activity.
So we have the dominance of the state, with ideas such as separation between church and state and religious liberty as justifications of modern government to suppress religion and enact their will completely unimpeded.
So people today take for granted the fundamental basis of Liberal Secularism and so it creates a dichotomy where conflict and warfare that pertains to things labeled political or state-ran are justified since they are secular and because of this many tolerate it or consider it acceptable base upon the fact that it is neutral.
Where conflicts arise from religion it is something that is an unspeakable barbarism and absolutely unjustifiable and that because it is motivated by a type of faith it is extremism and must be extirpated at all costs.
This is evidently seen where people find it completely normal and respectable that a person die for their nation yet those who have sacrificed themselves for their faith are seen as uncivilized and deserve all forms of vilification.
Although there is no real adequate definition of what exactly is religion so it is most of the time arbitrary, or is defined to suit the agendas of different people or justify the monopoly of the state.
In the west today what is given the title of religion is something that has been neutered and forced into the private sphere so that it has no say in political manners, and so conservatives take no note of them because they are no threat to the Liberal State’s Dominance.
So the many denominations of Christianity, Buddhism, Hinduism, ect… know to bow down before the Secular State’s control and so conservative has no problem towards them because they all know their place. So when Muslims assert the need for a Islamic State that abides by a law derived from their religion (Shariah), this drives conservatives into a fit of rage because there is a group that refuses to kowtow before Liberal Governance.
They have an assumption that religion is simply only one compartment completely isolated from all the other compartments of society where it only has a say in the areas of private practice or designated religious temples. That religion tries to assert itself outside of their little-corner is something that is detestable to them.
They simply define religion as a thing that is insignificant in the public/political realm and that is pacifistic and that is subordinate to a nonreligious governance.
Then they define ideology/politics as something that does and can assert itself publicly and politically and so they see an evil in Islam that tries to make itself so, since it does not stay in it’s lane.
They still believe in the myth that having the State separated from Church somehow is more peaceful and civilized when in fact secular liberalism with its government systems have killed more people than any other worldview in history.
What makes Islam different than Christianity is that there is no distinction between Church and State, the Church IS the State. However, historically there has been no clear line of demarcation that a religion can be extracted from its civilization context, this is just an modern fabrication. We have had fully holistic Catholic States, Islamic States, Buddhist States, ect where the religious aspects are impossible to removed from its governing structure since it is all integrated.
Christians are angry at Islam the same way a domesticated and neutered dog doesn’t like that wild wolf who doesn’t accept being petted and chained up in a doghouse by its master.