According to the Midrash (Ex. Rabbah 19:6), it was like a king who arranged a banquet for his friends and told his servants, “Unless the invited guests show my seal on the invitation card, they cannot enter”.
Thus God said to the Israelites, “Unless you possess the sign of Israelite identity you cannot eat my paschal lamb”.
The Midrash goes on to say that the uncircumcised elements who accompanied the Israelites immediately sought to be circumcised, and God took each one, kissed him and blessed him.
One could suggest that whenever there is a party everyone wants to be there, and that’s how to explain the whole episode.
But the Midrash is probably saying something much more serious, that being Jewish brings with it both agonies and ecstasies.
People who did not go through the times of suffering cannot hope to enjoy the times of fulfilment. It seems something like the Biblical law of the Sabbath (Ex. 20): “Six days shall you labour and do all your work, and (if you have carried that out) the seventh day is the Sabbath of the Lord your God”.
There are, for example, many well-intentioned Christians who say they would like to take part in a Jewish Passover celebration and of course we admire their good will, but a person who has not lived through Jewish history cannot possibly really appreciate the full spirit and meaning of the Seder celebration.