...[T]he Archbishop in the Kansas City area did not approve of my conduct as a public official and asked that I not present myself for communion.
Well, it was one of the most painful things I have ever experienced in my life, and I am a firm believer in the separation of church and state, and I feel that my actions as a parishioner are different than my actions as a public official and that the people who elected me in Kansas had a right to expect me to uphold their rights and their beliefs even if they did not have the same religious beliefs that I had. And that's what I did: I took an oath of office and I have taken an oath of office in this job and will uphold the law.
There is much to unpack here. Let's start with the "separation of church and state" bit. There is nothing in the Constitution about separating church and state; the closest there is is the First Amendment, which states (in part): "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof...." There is certainly nothing that says, "Elected officials must not inform their actions by their religious beliefs." Wouldn't that be a silly requirement? Other beliefs are not so proscribed. You might as well require a separation of philosophy and state.
Perhaps Sebelius simply means that, while there is no Constitutional requirement, she personally believes that her religious beliefs should be subordinate to the wishes of her constituents. But those who elected her presumably knew she was Catholic and that the Catholic church proscribes abortion, yet they elected her anyway. Furthermore, nowhere is it written that elected officials must always be perfectly aligned with their electorates (which would anyway be impossible). Edmund Burke wrote: "Your representative owes you, not his industry only, but his judgment; and he betrays instead of serving you if he sacrifices it to your opinion."
Finally, there is the bit where she says she will uphold the law. Perfectly fine, of course, except that the issue of abortion is hardly settled law. There is much activity in various corners that does not fall afoul of Roe v. Wade and subsequent decisions, which is one reason why abortion remains a major issue in elections to this day. A Catholic can oppose abortion to the extent possible under the law and presumably would not draw the ire of her Archbishop. The reason Sebelius got in trouble is that she did much to oppose pro-life positions in contravention of Catholic teachings.
Ultimately, Sebelius wants to portray herself as a heroine who remained loyal to her constituents and to the law even when disciplined by her church. But this is clearly not the case. She made a choice and paid the price.