Do you think it would be a good idea for our church to encourage the congregation to exercise their right to vote in elections occasionally? Personally, I consider voting a privilege and responsibility as a citizen and a christian...what do you believe?
I don't know if it's right or not, for Gateway leadership to purposefully encourage the congregation to vote (even occasionally, which I appreciate that you included that word in your question). With the divisiveness we have in our country over politics, I'd rather the congregation be hearing how our faith in Christ is the only hope we have for unity in our country. Yes, being able to vote is a privilege we have in the US, but the Bible seems to suggest that there are much more important responsibilities we have as Christians than to exercise our right to vote. Loving God and our neighbors come to mind. I'd rather those kinds of things to be what we focus on during our gathered time together.
Here's a link to a NY Times article by Tim Keller on Christians and our US political system that you may find helpful. What he articulates about the current pressure to "package deal ethics" is why I hesitate to bring up voting to our congregation. It's hard to not sound like I am fully endorsing (or condemning) one party or the other and I don't want a particularly political party to be what people first associate me with as this potentially closes off their ears to my sermons.
What then, about someone who has professed belief in Christ but is now living in unrepentant sin?
Your question is somewhat difficult to understand due to you beginning with "what then." I'm not sure what that is referring to from my sermon. Regarding someone who professes to believe in Jesus, but is now living in unrepentant sin, the Bible is clear of their situation. First John 3 comes to mind. "Everyone who makes a practice of sinning also practices lawlessness; sin is lawlessness. 5You know that he (Jesus) appeared in order to take away sins, and in him there is no sin. 6No one who abides in him keeps on sinning; no one who keeps on sinning has either seen him or known him. 7Little children, let no one deceive you. Whoever practices righteousness is righteous, as he is righteous. 8Whoever makes a practice of sinning is of the devil, for the devil has been sinning from the beginning. The reason the Son of God appeared was to destroy the works of the devil. 9No one born of God makes a practice of sinning, for God's seed abides in him; and he cannot keep on sinning, because he has been born of God." (1 John 3:4-9 ESV)
The phrases "practice of sinning" and "keeps on sinning" are referring to the unrepentant sin that you speak of. Yes, all people sin (even Christians), but to be purposefully unrepentant is to show that you have not been born of God (v9), which means that no matter what they may have professed with their mouth, their heart was not made new by God. Also, see Hebrews 10:26-27.
Question from Sunday's sermon: How do we know Abraham was once a pagan? Is there a biblical reference to directly support this or is it an assumption based on where he lived and what we know about that culture?
I've answered a similar question previously. You can find it, and my response, here.