Pregnancy termination is a controversial subject, even when extended to 'emergency contraception.' Would have any issues providing such treatment, especially in a case of rape or incest?

Rape and incest are traumatic physical assaults that also have the possibility of an unwanted pregnancy. Worse, the physicality and pregnancy risk can entail severe psychological repercussions. As such, eliminating the pregnancy risk has become an important consideration as part of the care for these patients. This only makes it more difficult if you're philosophically opposed to pregnancy interruption. The conflicting definitions of where life actually begins (i.e., conception, implantation, presence of a fetal heartbeat, etc.) may afford you some philosophical wiggle room, but you must be prepared for situations that will cross your personal red line.

Also, many ERs have specially trained nurse examiners for these delicate situations, so acknowledge you have no problem allowing them to take over.

Here is a sample answer with no objections:
'My role as an Emergency Medicine specialist is to put my patient first, given the traumatic effects, especially, of rape or incest. This means treating the problem fully, including addressing possible repercussions that could negatively impact my patient later. I also want to work with any specially trained team that takes part in her care.'

Here is a sample answer with objections:
'My role as an Emergency Medicine specialist is to put my patient first, given the traumatic effects, especially, of rape or incest. If there is a specialized team who address the patient, I have full confidence in their abilities and will gladly let them administer exams and care, including what would be done in regard to pregnancy potential. If such a team isn't available, cases in which I'm challenged to remain true to my own philosophical position would require me to simply recuse myself and have a colleague attend the patient.'