Context. This passage speaks of eating bread with unwashed hands.
Compare
CLV) 1Co 6:9
Or are you not aware that the unjust shall not be enjoying the allotment of God's kingdom? Be not deceived. Neither paramours, nor idolaters, nor adulterers, nor catamites, nor sodomites,
(CLV) 1Co 6:10
nor thieves, nor the greedy, nor drunkards; not revilers, not extortioners shall be enjoying the allotment of God's kingdom.
Context? Mark 7 opens with the Lord talking to the Pharisees and scribes about their oral traditions, which certainly included the extensive washings of hands, pots, cups, etc., and how some of their traditions are worse than useless, because they often invalidate the word of God .
The Lord then calls another group to come and listen to Him, the people of Israel, and He continues his conversation with them, which he ends by saying this, "
~whatever~ enters a man from outside cannot defile him, because it does not enter his heart but his stomach, and is eliminated, thus purifying all foods". This statement is hardly about hand washings.
I left you passages from St. Luke (Acts) and St. Paul (Romans) as well. Both passages make it clear that
ALL foods are now considered to be pure/clean, because the Lord God has made them so.
Again, there is no ambiguity whatsoever in these didactic statements (from either the Lord Jesus, St. Peter and/or St. Paul). That said, there is nothing wrong with keeping kosher if you'd prefer to do so (in and of itself anyway). If you don't mind me asking, do you keep Torah? And if you do (and if you don't mind me asking), why do you do so/what is your principle purpose in doing so?
Thanks again!
--David
p.s. - you posited
1 Corinthians 6:9-10 for comparison, but I'm not sure why you did (since none of the sins listed there concern what we eat)

Perhaps you could elaborate a bit?