In Exodus, God was giving commandments for the very first Passover. In this first Passover God did not want strangers to partake of it. However, later on in Numbers, this restriction was lifted. Sincere strangers who wanted to perform the Passover could do so.
God can certainly lift or modify restrictions, and so this is not a contradiction. Perhaps the first Passover was meant to be extra special; or perhaps no strangers sincerely believed in God at that time, whereas strangers who followed the Israelites throughout the wilderness were much more likely to be sincere. In any case, God had special requirements for the very first Passover.
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