Hi Doug,
Well without going into exactly what Ray said or didn't say, I will reply to the general question you pose. Actually this question is comparing 2 totally different things.
Voting is part and parcel of the politics of a government, which is totally worldly/carnal in nature. To vote is desiring to influence how a government operates.
James 4:4 You adulterous people! Do you not know that friendship with the world is enmity with God? Therefore whoever wishes to be a friend of the world makes himself an enemy of God.
Here is a definition of Friend - One who supports, sympathizes with, or patronizes a group, cause, or movement.
If we are to come out and be separate, why would we want to be involved/friendly with worldly goings on?
2Co 6:14 Do not be unequally yoked with unbelievers. For what partnership has righteousness with lawlessness? Or what fellowship has light with darkness?
v. 15 What accord has Christ with Belial? Or what portion does a believer share with an unbeliever?
v. 16 What agreement has the temple of God with idols? For we are the temple of the living God; as God said, "I will make my dwelling among them and walk among them, and I will be their God, and they shall be My people.
v. 17 Therefore go out from their midst, and be separate from them, says the Lord, and touch no unclean thing; then I will welcome you,
v. 18 and I will be a father to you, and you shall be sons and daughters to me, says the Lord Almighty."
As for praying to be healed, that is a personal matter. Since we do not know what God's will is, it certainly may be for somebody to be healed as the results of a inspired pray request.
James 5:13 Is anyone among you suffering? Let him pray. Is anyone cheerful? Let him sing psalms.
v. 14 Is anyone among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord.
v. 15 And the prayer of faith will save the sick, and the Lord will raise him up. And if he has committed sins, he will be forgiven.
v. 16 Confess your trespasses to one another, and pray for one another, that you may be healed. The effective, fervent prayer of a righteous man avails much.
mercy, peace and love
Kat