Everyone, at some time or another, is hypocritical. Left, right, conservative, progressive, you, me... It happens. Such is life.
The real issue with conservatives today, though, is that they have largely unified behind the Republican Party, which is in thrall to the plutocrats. Note that in the past, the parties were more ideologically diverse -- there were conservative Democrats, and moderate and liberal Republicans. This causes a few issues.
One, Republican elected officials have pressed harder and harder on white grievance, racist, sexist, xenophobic views as their primary policies (cutting taxes for the wealthy and corporations; deregulation; cutting safety nets; opposing single payer health care etc) are increasingly unpopular.
Two, this often results in promises to social conservatives that rarely result in actual policies -- hence the hypocritical worship of Trump by evangelicals, because he's giving them a few crumbs off the table.
Three, Trump's inept authoritarianism and cult of personality is based on a total disregard for any sort of truth, accuracy, fairness or consistency. Everything except a one-way demand by Trump for loyalty goes out the window. Thus, anyone who sides with him for more than two minutes is forced to adopt hypocritical positions. Character matters, but not when it comes to a thrice-divorced serial adulterer; deficits are terrible and will destroy the nation, but not when Trump is in office; mail-in ballots will destroy the nation, but it's OK when Trump votes repeatedly by mail.... I could literally be here all day citing instances where people need to violate their own values and long-held political positions, because they expect Trump will do something they want, or are afraid to criticize him.
However, this is NOT a result of a specific ideology, it's a result of autocracy. We see the same conditions in autocrats around the world, whether they are right-wing (Peron, Duterte), Communist (Castro, Stalin), leftist (Correa, Maduro), whatever.
This is because for an autocrat, truth doesn't matter, and lies serve primarily to distract the opposition and express power. The poor suckers who work for or support the autocrat are thus forced to contradict themselves on a daily basis, primarily as a constant loyalty test and distraction method.