It is not possible for a reasonable Conservative to exist, because Conservativism isn’t a reasonable ideology. There are no permanently conservative priorities, because each conservative defines conservative values around their own definition for who is included in their version of conservativism.

I know you’re probably running down a list in your head of all the values that you associate with stereotypical conservatives, but there isn’t one of them where you won’t find exceptions and rationalizations for why it’s OK for conservatives to ignore those values. Their position inevitably changes when the position is not benefiting their in-group. They are anti-abortion, until they want an abortion. They are anti-inmigration, except for immigrants from their home country. They want low taxes, for themselves, and want to reduce spending on anything they don’t directly benefit from.

Just about the only thing you could argue is exclusively conservative are most forms of bigotry. While there are certainly bigoted progressives, bigots are welcomed and supported in Conservative parties as long as they fit within the defition of the self.