The word 'ideology' has negative connotations, associated as it is with the polarization of political opinion and consequent breakdown of social cohesion. But arguably we all have an ideology of sorts - a value-system related to social and political matters - implicit if not explicit.
Genetic and environmental influences all play a role in predisposing one towards the left, right or other putative dimensions on the political scale. And there is not much one can do about that, other than to be aware that such influences are potent. One should definitely not take one's social and political views to be self-evident.
Without denying the very real differences between them, intelligent liberals and conservatives can agree on a number of important things - for example, the desirability of good manners, the need for long-term fiscal planning and the need for some kind of system to assist those who have been afflicted by acute misfortune or who simply cannot cope.
Extreme views are problematic. It seems to me that those who hanker for some kind of revolutionary (or reactionary) apocalypse are beyond the pale, probably harmless dreamers and schemers, but just possibly dangerous. For there are dark depths in all our minds and sometimes one senses primal resentments (and psychological problems) behind the words and actions of extremists, whether they be loners or members of extremist groups.
So much of the trouble in today's world is based on ethnic grievances, and the kind of group-think encouraged by many supposedly oppressed groups feeds these resentments and easily erupts into violence.
I identify as a conservative, but, like many conservatives, I also draw on the classical liberal tradition. Unfortunately, the word 'liberal' has been effectively hijacked by those with 'progressive' opinions, many of which have little to do with the freedom of the individual (a commitment to which lies behind classical liberalism) and much to do with the machinations of advocates for 'oppressed' groups.
From my point of view, there is something very powerful and positive about the old liberal notion of blind justice - treating everyone simply as a person rather than as a representative of a group or class. I know all the arguments about unconscious bias and structural inequities, but identifying as oppressed, identifying with a particular oppressed group, is, I think, in most cases counterproductive to the well-being of the individual or family in question. I have the strong sense that those from disadvantaged backgrounds etc. who refuse to dwell on these matters and just get on with their lives are giving themselves a far better chance of success and happiness. Advocacy for women and various ethnic groups has become an industry in the West, and just who this industry serves is a moot point.
Despite inevitable differences between conservatives and liberals, the old-fashioned liberalism espoused by many conservatives creates the potential for productive dialogue between these liberal conservatives and old-fashioned - or conservative - liberals.