I have to give another POV here... keep in mind that I am a math geek, and my dd seems to be too.
I really like Horizon Math. I've used K, 1, 2, and 3, and will be purchasing 4 soon. One of the things I like about it is that it is a bit more advanced than some of the other programs I've seen. I will use it for my youngers when they are ready.
There were some things that I prefer to present differently than they have, but I figure that would be the same in any math curriculum. And I have occasionally crossed out an example, and have even crossed out a section here and there, but not frequently at all.
The teacher's manual is helpful for those who need something scripted for them. I have the teachers manuals, but don't really use them, since most times my dd has already been taught a concept by me prior to us getting to it on paper anyway (did I say I was glad it was advanced?).
I do prefer for dd not to do all the review problems, and do tend to cross out a lot of those, but that is my preference for THIS child. I don't know that I will do the same for the others, as I don't know what they will need.
Horizon does stress mastery of math facts/tables as well as counting by every number up to 12s. Some like this, some don't. I like it. I think knowing these well makes high level math easier.
Everything I have seen Horizon present has a view toward using it in the future, for higher level math, which I really like. Of course, this isn't something my dd sees, but I see it as an adult. This makes learning new concepts easier, since it builds on a concept they've already mastered.
I don't think it is super teacher intensive, but the TM does have you go over a problem, then have them complete the rest, then move onto the next section. I have often done the lesson on a separate piece of paper, then had her complete the worksheet. There is not usually more than one new concept on each lesson. Review for other sections is dependent upon your child.
As far as the Christian presence... I think I saw ONCE when introducing ordinal numbers, the days of creation (1st day, 2nd day, 3rd day, etc.).
HTH!