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Yes, the context was the washing of hands. But he's obviously not talking about hand-washing per se; he's talking about "defiled food" (which passes into the stomach and is expelled).

The context is indeed ritual washing. And Jesus told his disciples and us what he meant:

Mat 15:16 And Jesus said, Are ye also yet without understanding?
Mat 15:17 Do not ye yet understand, that whatsoever entereth in at the mouth goeth into the belly, and is cast out into the draught?
Mat 15:18 But those things which proceed out of the mouth come forth from the heart; and they defile the man.
Mat 15:19 For out of the heart proceed evil thoughts, murders, adulteries, fornications, thefts, false witness, blasphemies:
Mat 15:20 These are the things which defile a man: but to eat with unwashen hands defileth not a man.

The issue was ritual washing of hands, a tradition that Jews invented, not something scripturally commanded. The food laws, on the other hand, were something that Christ himself commanded.

Your interpretation, though common, is a mistake in that it is done through a prism of tradition that disagrees with biblical precepts and practices.

Mark:18-19
And He said to them, "Are you so lacking in understanding also? Do you not understand that whatever goes into the man from outside cannot defile him, because it does not go into his heart, but into his stomach, and is eliminated?" (Thus He declared all foods clean.)

It seems that Mark once again disagrees with your assessment, as well as Peter's vision, but that's OK. If you wish to observe the food laws, then go right ahead, but we are clearly shown that all foods have become clean.

We live, like you said, under Grace. Feel free to eat the foods that you wish. If you feel that certain food are verboten or can cause stumbling blocks, then by all means avoid them.

Romans 14:3-13
3 The one who eats is not to regard with contempt the one who does not eat, and the one who does not eat is not to judge the one who eats, for God has accepted him.
4 Who are you to judge the servant of another? To his own master he stands or falls; and he will stand, for the Lord is able to make him stand.
5 One person regards one day above another, another regards every day alike Each person must be fully convinced in his own mind.
6 He who observes the day, observes it for the Lord, and he who eats, does so for the Lord, for he gives thanks to God; and he who eats not, for the Lord he does not eat, and gives thanks to God.
7 For not one of us lives for himself, and not one dies for himself;
8 for if we live, we live for the Lord, or if we die, we die for the Lord; therefore whether we live or die, we are the Lord's.
9 For to this end Christ died and lived again, that He might be Lord both of the dead and of the living.
10 But you, why do you judge your brother? Or you again, why do you regard your brother with contempt? For we will all stand before the judgment seat of God.
11 For it is written, "AS I LIVE, SAYS THE LORD, EVERY KNEE SHALL BOW TO ME,AND EVERY TONGUE SHALL GIVE PRAISE TO GOD."
12 So then each one of us will give an account of himself to God.
13 Therefore let us not judge one another anymore, but rather determine this--not to put an obstacle or a stumbling block in a brother's way.

JM