"Those excluded from the Congregation" Deuteronomy 23:1-8 lists some people that are forbidden to "enter the assembly of the LORD".


  Deuteronomy 23:1-8 (NKJ)
  
  Those Excluded from the Congregation
  
  1 “He who is emasculated by crushing or mutilation shall not enter
  the assembly of the LORD. 2 “One of illegitimate birth shall not enter
  the assembly of the LORD; even to the tenth generation none of his
  descendants shall enter the assembly of the LORD.  3 “An Ammonite or
  Moabite shall not enter the assembly of the LORD; even to the tenth
  generation none of his descendants shall enter the assembly of the
  LORD forever, 4 because they did not meet you with bread and water on
  the road when you came out of Egypt, and because they hired against
  you Balaam the son of Beor from Pethor of Mesopotamia, to curse
  you. 5 Nevertheless the LORD your God would not listen to Balaam, but
  the LORD your God turned the curse into a blessing for you, because
  the LORD your God loves you. 6 You shall not seek their peace nor
  their prosperity all your days forever.  7 “You shall not abhor an
  Edomite, for he is your brother. You shall not abhor an Egyptian,
  because you were an alien in his land. 8 The children of the third
  generation born to them may enter the assembly of the LORD.


What is the meaning of this? How should it be interpreted? Should this be applied today? If so, how?
You have to go all the way back to Deuteronomy 12 to get to the beginning of the &quot;statutes and judgments&quot; given by God to the Israelites.

Deuteronomy 12:1-7(NKJ)
A Prescribed Place of Worship
1 “These are the statutes and judgments which you shall be careful to observe in the land which the LORD God of your fathers is giving you to possess, all the days that you live on the earth. 2 You shall utterly destroy all the places where the nations which you shall dispossess served their gods, on the high mountains and on the hills and under every green tree. 3 And you shall destroy their altars, break their sacred pillars, and burn their wooden images with fire; you shall cut down the carved images of their gods and destroy their names from that place. 4 You shall not worship the LORD your God with such things.
5 “But you shall seek the place where the LORD your God chooses, out of all your tribes, to put His name for His dwelling place; and there you shall go. 6 There you shall take your burnt offerings, your sacrifices, your tithes, the heave offerings of your hand, your vowed offerings, your freewill offerings, and the firstborn of your herds and flocks. 7 And there you shall eat before the LORD your God, and you shall rejoice in all to which you have put your hand, you and your households, in which the LORD your God has blessed you.

Emphasis mine.
God is giving instruction appropriate for the time and the place.  Not everything in Deuteronomy is appropriate for our time and our place.
As J. Daniel Hays writes in his Applying the Old Testament Law Today:

The narrative setting for the Book of Deuteronomy is the eleventh month of the fortieth year of the Exodus (Deut. 1:3), just before Israel entered Canaan. The place is specified—just east of the Jordan River (1:1, 5). Israel had completed the forty years of wandering as a punishment for refusing to enter the land. Now a new generation had grown up and God gave them a restatement of the covenant that He had made with their parents forty years earlier. Most of Deuteronomy consists of a series of speeches that Moses delivered to the Israelites on God’s behalf. These speeches are connected to the narrative because they refer to the same time, place, and main characters as the narrative does. Also the end of the book contains some nonlegal, narrative material: the appointment of Joshua as leader (31:1–8), the song of Moses (32:1–47), a blessing of Moses on the tribes (33:1–29), and the death of Moses (34:1–12). Furthermore the events of Deuteronomy flow into the Book of Joshua, where the story continues without interruption.