Amen. Just saying I've heard that use from other moderates as well who don't think too hard about it.
Anyway, the other question is the more interesting to me. Any good left-leaning or socially-conservative-fiscally-liberal (short name?) news source?
The American Conservative is definitely socially conservative and, if not exactly fiscally liberal, at least much more sympathetic to economic redistribution than mainstream conservatism. But it is more composed of opinion pieces than of news reports, so I don't know if it works for way you want.
As others suggested, Vox could be a good choice for a left-leaning news source. It has decent summaries of "everything you need to know about X" (where X = many current news stories).
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.