I see no inconsistency, just conservative doublespeak.
Their rant against the usage of abortion terms in the Stylebook simply proves the author's ignorance (note, I say the author, not conservatives in general). The term "anti-abortion" perfectly describes that political movement without using political catchphrases. "Pro-life" rarely describes the anti-abortion camp, as many of them don't care what conditions the baby has to live in once they're born, and advocate for the termination of social programs that help babies (and mothers) living in squalor. Don't even bother asking them about the death penalty: the Bible says "an eye for an eye," so most of them are for it. Nothing about this says "pro-life."
On the liberal side, "abortion rights" means exactly what it says: the right to have an abortion. "Pro-choice" is kind of wishy-washy. We all know what the choice is, but the term by itself isn't the slightest bit descriptive to anyone who may never have heard it before. And "pro-abortion" is a conservative jab meaning "you want to kill babies, you wretched monsters." The Stylebook merely advocates clarity of prose over politicization.
The Stylebook's stance on transsexuals is not politicization, but a reflection of modern science's findings in the area of transsexual biology. Ah, there's that word the author of this op-ed has such a problem with: biology. If he knew anything at all about biology and science, it's that everything is a theory, because, technically, everything has the potential to be disproven and/or modified based on new research. Apparently, nothing can ever go wrong biologically, according to this author. Everything is cut-and-dry, perfectly compartmentalized, and without deviation. Cells are cells, right? They replicate like they should, right? So cancer must not exist either. Or should the Stylebook refer to it as "cancer?" (in quotes, because cancer patients are obviously just faking this biological aberration of a natural process for political gain). Maybe cancer patients should be referred to as "leeches of the medical system" or "people who drive insurance costs up." After all, everything should work perfectly! It's biology!
Gah, the ignorance of this piece confounds me.