How does leaving a 'gift at the altar' reconcile with reformed views of the need to 'approach the throne of grace' in everything? Jesus said:


  “Therefore, if you are offering your gift at the altar and there remember that your brother or sister has something against you, leave your gift there in front of the altar. First go and be reconciled to them; then come and offer your gift. (Matthew 5:23-24, NIV)


However, this might make someone infer that while we have any 'big sin' in our life, like hateful anger for a brother, we should reform our life before approaching God. Clearly such a works based concept is absolutely opposed to the gospel. So the question is what is a valid exegesis of Mathew 5:23-24 that does not conflict with our need to approach the throne of grace to enable this 'leaving the gift at the altar' and attempt of reconciliation with a brother?

Is there any sin that we must straighten out before approaching the throne of grace?

Note: I was first tempted to ask this question on BH.SE but I realized although asking for an exegesis, this is actually exploring the entire theological framework of reformed theology because the belief that one may have to take care of any sin first, and then approach God is in direct conflict with a reformed position and so the question is more theological than exegetical.
this is actually exploring the entire theological framework of
  reformed theology using this particular verse only


That's a bad idea from a Reformed or any other perspective.  To take one verse and attempt to understand a full theology based on it is simply not possible.  The surest way to misinterpret Scripture is to take verses out of context.

Taken in context, this is not speaking about straightening out a specific sin prior to going to the altar, it's about the principle of going to the alter to "worship" with a heart that's far from God.  It's a perfect complement to Hosea 6, which speaks of Israel turning to God with an unrepentant heart simply to achieve personal gain - the healing of their land.  God rejects this, and in verses 6-10, we see the underlying principle:


  6 For I desire mercy, not sacrifice,
      and acknowledgment of God rather than burnt offerings. 7 As at Adam,[b] they have broken the covenant;
      they were unfaithful to me there. 8 Gilead is a city of evildoers,
      stained with footprints of blood. 9 As marauders lie in ambush for a victim,
      so do bands of priests; they murder on the road to Shechem,
      carrying out their wicked schemes. 10 I have seen a horrible thing in Israel:
      There Ephraim is given to prostitution,
      Israel is defiled.


This has nothing to do with salvation, predestination, or any other Calvinistic doctrine.  It has to do with the truth of the condition of our hearts.  It speaks to the pointlesness of following religious ritual, and the superiority of a heart that is turned over to God.  Such a heart will understand that love, kindness, and forgiveness are necessary, and will not worship in vain.

From Calvin's commentary:


  It amounts to this, that the precept of the law, which forbids murder,
  (Exodus 20:13,) is obeyed, when we maintain agreement and brotherly
  kindness, with our neighbor. To impress this more strongly upon us,
  Christ declares, that even the duties of religion are displeasing to
  God, and are rejected by him, if we are at variance with each other.
  When he commands those who have injured any of their brethren, to be
  reconciled to him, before they offer their gift, his meaning is, that,
  so long as a difference with our neighbor is kept up by our fault, we
  have no access to God. But if the worship, which men render to God, is
  polluted and corrupted by their resentments, this enables us to
  conclude, in what estimation he holds mutual agreement among
  ourselves.


It's not a legalistic "do this, get that" type of thing.  There is no "specific sin" to be taken care of first.  It is, as Christ is trying to teach in this passage, a matter of hypocrisy vs. true Christian love, which is a result of faith in God and repentance.