It seems to me that many people in Zen Practice have come to confuse "being present/mindful in the moment" (for example, "when drinking tea, just drink tea" ... a sometimes appropriate and lovely way to experience life) ... with "being at one with the moment" (allowing and merging with conditions of life "just as they are"). The two are not quite the same, and are often confused, and the latter is much more at the heart of this Shikantaza Path ...
Yes, I believe that there are times to be "mindful" ... and there are times not. Sometimes when I eat, I just eat ... when I sip tea, I just sip tea ... when bowing, just bowing ... fully absorbed in that action. A wonderful, insightful practice. When doing one thing, just do one thing with all one's body-and-mind.
At other times, I just grab a sandwich and a coke while reading the newspaper and thinking about the job I have to do. That's life too. Nothing wrong with it.
(I do not know where the idea started among some folks that the 'goal' of this practice is to live the first way every moment of every day. That would be pretty awful (if not harmful) to live like that all or even most of the time. What's wrong with also sometimes reading the paper, thinking about work, while grabbing a quick sandwich? There is a place for all of that.)
Further, people get even more confused about "mindful" in Buddhism because the word is used in a couple of distinct ways.
Another, rather different meaning of "mindful" often found in Buddhism is to develop awareness of the "mind theatre" running constantly in our heads (developing the ability to identify the thoughts and emotions that play through our heads, and how they create our experience of "reality" ... e.g., "now I am temporarily sad" "now I am reacting with anger") That is a wonderful, insightful practice too ... very very important ... but I caution against thinking that you must or can do that 24/7.
In my view, the heart of this Practice is merely "being at one" with this self-life-world just as it is ... dropping the resistance, barriers, separation between our "self" and all the circumstances in which that "self" imagines it finds itself in ... until even the walls between "self" and "life-world" (or self and itself) soften or even fully drop away ...
So, for example, when drinking tea, just do that and fully allow that. When grabbing a sandwich while reading the paper and thinking about your annoying co-worker in the office, just do that and fully allow that (and fully allow the craziness in the newspaper and your annoying co-worker too).** When your kid plops in your lap during tea drinking and the cup spills all over the table, just do and allow that. When your kid again plops in your lap during Zazen. ( http://www.shambhalasun.com/sunspace/?p=16432 ) When temporarily falling into sadness or anger, just do and allow that (although remember that "mind theatre" and see if you truly need to be that way, and seek to be not that way if you can). When overwrought with life for a moment, just do that and fully allow that (remembering in the back of your mind that the clear, boundless blue sky is behind the clouds of thought and emotion even when momentarily covered over). When suffering with old age and sickness of ourself or someone we love, even death, just do that and fully allow that.
In my view, all of the above together is truly balanced, "mindful" living. That is "being the moment".
** PS - "fully allowing" does not mean necessarily "fully allowing". We have something called "acceptance-without-acceptance" around here ... So, for example, we can "fully allow and be one with" the wars and pollution described in the newspaper or the bothersome person at work or the sickness we are suffering ... yet take steps to deal with each too. Not mutually exclusive perspectives.