I'm very calculating. I have shots calibrated for lots of situations, they are repeatable. I know my yardages for each club - full swing and partials. I know how much face and stroke is needed to carry pitches specific yardages and how much to change the setup to adjust a bit around those distances. (then it's just about executing those swings each time, isn't it? and that's not easy without some natural feel. still working on it.). I think hacking on someone for doing this is likely just someone too lazy to go figure it out and they resent the work others put in on it. I think people are very disadvantaged if they don't 'really' understand the physics of what's going on.
I'm very intuitive. Once I get the club and swing selected based on my practice and the above knowledge, I need to visualize the shot correctly. In odd situations, I need to be flexible enough to change up those 'standard' setups if the situation calls for it. However, if you don't take the time to understand the physics, then a self proclaimed "intuitive" golfer is really just guessing.
No, being 'very' both, is not a conflict at all.
Clearly, we all prefer to hit our "set shots" than to make it up as we go along. At least if we are looking for consistency. However, it's a lot more fun to 'make it up' as we go along. You never know what cool shots you might pull off.