My views do not depend on eschewing emotions, but rather, carefully navigating them. Emotions are a wonderful and valuable tool of the human intellect. I believe that if one does not pay attention to emotion, one cannot be fully informed.
The problem is that the more we learn about human intellect the more we learn that emotions can be false. In particular, the problem is that false emotions do not feel any different to us in terms of accuracy. Something can feel so very right while in fact be very wrong. Emotions can be helpful as a sort of executive function indicating what we should do with information once it is verified, but they cannot be relied on to separate what is so from what is not. This isn't just because they are unreliable, but also because, in so many cases, they seem geared to lead us in the opposite direction of truth.
That emotions are useful is actually part of the problem. I say that because in terms of evolution what's useful is not necessarily what is accurate. Protecting ego, ensuring social status and succumbing to superstition are also useful in the right situations. The older parts of our cognition, the ones that rule silently and supremely, are not interested in rationality, they are interested in what's useful.
So yes, thinking and feeling should never be separated, but the fact that something feels right is indication that the something is useful, not that it's true.
