Did God in Bible days not let disease and disability affect people in His church?
I believe you are referring to: "And the LORD will take away from you all sickness, and will afflict you with none of the terrible diseases of Egypt which you have known, but will lay them on all those who hate you" (Deuteronomy 7:15). This was a promise that God made to Israel just before they entered the promised land. This promise, however, was conditional: "Therefore you shall keep the commandment, the statutes, and the judgments which I command you today, to observe them. Then it shall come to pass, because you listen to these judgments, and keep and do them, that the LORD your God will keep with you the covenant and the mercy which He swore to your fathers" (Deuteronomy 7:11-12). God would do great and marvelous things for His people if they obeyed God. God had also promised to do the opposite if they disobeyed Him. "The LORD will strike you with the boils of Egypt, with tumors, with the scab, and with the itch, from which you cannot be healed. The LORD will strike you with madness and blindness and confusion of heart. ... The LORD will strike you in the knees and on the legs with severe boils which cannot be healed, and from the sole of your foot to the top of your head" (Deuteronomy 28:27-28, 35).
Sadly, they did not obey God and God kept His promise.
A similar promise about diseases was not made in the New Testament. The blessings in the New Testament emphasize the spiritual blessings of being freed from the disease of sin. "Blessed be the God and Father of our Lord Jesus Christ, who has blessed us with every spiritual blessing in the heavenly places in Christ" (Ephesians 1:3).