Why do people expect Muslims to apologize for the Taliban's actions yet don't expect Christians to apologize for the IRA's actions?

The IRA isn't a "Christian" group.  The conflict between the Irish and British was essentially a colonial issue.  The IRA never used Scripture to justify violence.

The Taliban, ISIS, Boko Haram, Al Shabaab, Al Qaeda and other fundamentalist Muslim terrorist organizations cite the Koran as justification for violence and rape.  They use the Koran to justify rape of non-Muslim women and children, violent attacks on non-Muslims and the Sunni's justify the many bombings against Shi'ite.  There are sects of Islam that are persecuted in Iran, as well.

I don't think ordinary Muslims need to apologize, but maybe wonder why there are elements in their religion that celebrate barbarism. 

I think all religions are a bunch of garbage any way.

Racism mostly. We in the west tend to forget all the bad things we've done in the past but we tend to hang onto the bad things committed by others. America is the biggest culprit of this. As the comedian Louie C.K. said, Americans are like the "shitty girlfriend of the planet. We forget everything bad we've ever done but we remember EVERYTHING that people ever did to us." So in essence, we expect Muslims to apologize because we remember what they have done wrong but we don't expect Christians to apologize because we forgot that they ever did anything bad. 

And either way neither religion will apologize because neither group sees these terrorists as being true parts of their religion. Mainstream Muslims don't recognize ISIS as being "true" Muslims and mainstream Christians don't recognize the IRA as being "true" Christians. Nobody likes their weakest link. No church or mosque in civilized society is willing to claim radicals as their own. 

Asking either faith to apologize for their radical minorities won't work because neither religion thinks of these terrorists as being true to the faith.

The question is flawed, because it's based on a flawed premise.

Nobody expects Muslims to apologize for the actions of the radicals … they expect them to decry those actions.  The same way Christians will decry the actions of radical Christian groups - such as those Westboro idiots.

It's Catholics, not all Christians.

They are civilized enough to sit and discuss a settlement.