It is true that God specifically states in the Torah that no uncircumcised person is allowed to EAT the Passover sacrifice. More specifically:
There shall no stranger eat thereof...
Then He continues to explain the ordinance of the slave foreigner (who was bought with silver) partaking in Passover. Then God says:
when a stranger shall sojourn with thee...
I read this as a continuation of the exception of the law "no stranger shall eat thereof", that slave foreigners who are sojourning with the Israelites must become circumcised before eating the Passover sacrifice.
But every man's servant that is bought for silver, when thou hast circumcised him, then shall he eat thereof.