Should we "ignore" feelings while being mindful and aware of the present moment? When I am not judging any moments of life and taking it all in, should I give importance to feeling anything at all? I tend to get very rational and "accepting" about things. A feeling of letting go arises, which makes me feel very passive? It feels like there is no time for a feeling because we are losing the next moments by living inside a feeling, either positive/negative.

Also am I doing this right? Sometimes, it is like I am shutting that emotion up because I don't want to give in to a feeling. Why would I not want to give in to a feeling that makes sense at that point of time? That is mere repression.

Any thoughts on this?
Any experience you should be equanimously and objectively aware of perceiving (desirable, undesirable, neither) and sensation (pleasant, unpleasant and neutral) of the arising and passing or the sensation devoid of any craving or clinging while keeping though proliferation in check.

When you let go there is a feeling of renunciation with again is 3 types according to Sal-āyatana Vibhanga Sutta. A house holder seeks sensual pleasure and is temporarily satisfied or unsatisfied by the experience by perceiving and desirable or undesirable or neither. When you renounce householders life you strive to stop this perceiving by understanding the universal characteristics of the experience (changing, unsatisfactory, non self). In this letting go there is a pleasure also whis is non sesual nature. See: Sal-āyatana Vibhanga Sutta, Pañcak’aṇga Sutta, Bahu,vedaniya Sutta

There are 18 mental examination:


  (1) On seeing a form with the eye,
  one explores a form that gives rise to pleasure,
     one explores a form that gives rise to pain [displeasure],
        one explores a form that gives rise to equanimity.
  
  (2) On hearing a sound with the ear,
  one explores a sound that gives rise to pleasure,
     one explores a sound that gives rise to pain [displeasure],
        one explores a sound that gives rise to equanimity.
  
  (3) On smelling a smell with the nose,
  one explores a smell that gives rise to pleasure,
     one explores a smell that gives rise to pain [displeasure],
        one explores a smell that gives rise to equanimity.
  
  (4) On tasting a taste with the tongue,
  one explores a taste that gives rise to pleasure,
     one explores a taste that gives rise to pain [displeasure],
        one explores a taste that gives rise to equanimity.
  
  (5) On feeling a touch with the body,
  one explores a touch that gives rise to pleasure,
     one explores a touch that gives rise to pain [displeasure],
        one explores a touch that gives rise to equanimity.
  
  (6) On cognizing a mind-object with the mind,
  one explores a mind-object that gives rise to pleasure,
     one explores a mind-object that gives rise to pain [displeasure],
        one explores a mind-object that gives rise to equanimity.
  
  Thus there are six mental explorations with regards to pleasure; six mental explorations with regards to pain [displeasure]; six mental explorations with regards to equanimity.
  ‘The 18 kinds of mental explorations should be understood,’ thus it is said in this connection.


See: Sal-āyatana Vibhanga Sutta, Titth’ayatana Sutta, Dhātu Vibhaṅga Sutta, Indriya Bhāvanā Sutta

Where you have to examine the sensations hence you doing it right. This plays a role in removing the roots. See: Pahāna Sutta, Avijja Pahana Sutta 2