What would you tell an eldership who thought that it would be divisive to have me as a minister? I mean I don't want to make an issue of it. Shaina my future wife would wear a headcovering, but I would not teach something the elders do not want me to. I just didn't know who else to ask for their opinion on such a strange matter.
I would probably quote Romans 14:4-13, "Who are you to judge another's servant? To his own master he stands or falls. Indeed, he will be made to stand, for God is able to make him stand. One person esteems one day above another; another esteems every day alike. Let each be fully convinced in his own mind. He who observes the day, observes it to the Lord; and he who does not observe the day, to the Lord he does not observe it. He who eats, eats to the Lord, for he gives God thanks; and he who does not eat, to the Lord he does not eat, and gives God thanks. For none of us lives to himself, and no one dies to himself. For if we live, we live to the Lord; and if we die, we die to the Lord. Therefore, whether we live or die, we are the Lord's. For to this end Christ died and rose and lived again, that He might be Lord of both the dead and the living. But why do you judge your brother? Or why do you show contempt for your brother? For we shall all stand before the judgment seat of Christ. For it is written: "As I live, says the LORD, Every knee shall bow to Me, And every tongue shall confess to God." So then each of us shall give account of himself to God. Therefore let us not judge one another anymore, but rather resolve this, not to put a stumbling block or a cause to fall in our brother's way" (Romans 14:4-13). But then I'm a fairly direct-to-the-point type of preacher.
There are two things wrong with your situation. You have an eldership who are more interested in conformity than in determining exactly what God does and does not allow. If they truly believe the headcovering is not necessary, then it shouldn't make a difference to them if someone chooses to wear a covering. Nor should it matter if the issue is discussed, so long as each person is polite, willing to look at the Scriptures, and respectful towards each one's decision. As an example, my wife and I believe that God wants women to wear a headcovering while praying, so do several others in the congregation. But that belief is not held by the whole, yet we worship together in peaceful harmony. The topic is discussed periodically, mostly one-on-one as individuals are curious as to why. None here say that a woman cannot attend if she doesn't wear a covering as that would defeat the purpose of the covering. Nor are there any here who insist that women not wear the covering because they see that the choice doesn't impact their own worship in any way. Given the attitude of the eldership, I would seek out a congregation that displays a greater love for brethren with which to work. This is just one minor issue, but it probably is an indication of deeper problems which are hidden at the moment.
The second thing is that I recommend that you restudy the relationship between a preacher and the eldership. The elders' duty is to watch over God's people and to direct them to heaven. A preacher's duty is to teach God's word in its entirety. "And indeed, now I know that you all, among whom I have gone preaching the kingdom of God, will see my face no more. Therefore I testify to you this day that I am innocent of the blood of all men. For I have not shunned to declare to you the whole counsel of God" (Acts 20:25-27). As a preacher, you are a herald for the Lord Jesus Christ. You work for the king, not the eldership of a congregation. The elders will be concerned about the accuracy of your teachings because they have a duty to protect the flock from false teachers. They may request topics that they see is a current need among the flock or that hasn't been covered recently. But elders go beyond their authority when they tell a preacher that certain topics are not to be discussed. If a preacher is teaching false doctrine, they should discuss it with him and if he persists, they should dismiss him, just as they would withdraw from any member who spreading false teachings.
I remember during my teenage years being at a congregation that was looking for a preacher to work with them. One man came and during the meeting with him a brother asked him what subjects he planned on teaching now that he had seen the church. The man's answer was "I'll teach whatever the brethren here want me to teach." The room became instantly chilly because that was precisely the wrong answer. "I charge you therefore before God and the Lord Jesus Christ, who will judge the living and the dead at His appearing and His kingdom: Preach the word! Be ready in season and out of season. Convince, rebuke, exhort, with all longsuffering and teaching. For the time will come when they will not endure sound doctrine, but according to their own desires, because they have itching ears, they will heap up for themselves teachers; and they will turn their ears away from the truth, and be turned aside to fables" (II Timothy 4:1-4). We couldn't rid ourselves of him fast enough. Preaching the whole counsel of God means there will be times when you have to teach things that people don't want to hear. There will be times people will be mad at you, not because you said something unscriptural, but because you brought up points they didn't want to face. If you are going to be an effective preacher for Jesus, you are going to have to weather storms; a reading of Acts should make that clear to you. People are not going to like to hear the truth all the time.
There are numerous good, sound congregations looking for a hard working preacher who is willing to help them grow. Keep looking for a place where you are certain you will be effective. One of the interesting things that Jesus told his apostles to do when he sent them out was not to make a fuss when a city rejected them. "When they persecute you in this city, flee to another. For assuredly, I say to you, you will not have gone through the cities of Israel before the Son of Man comes" (Matthew 10:23). That advice remains true. You only have a few short years to preach. There is far too much work to be done; more work than you can accomplish in a lifetime. It isn't worth wasting time in a place you aren't wanted. Move on to where you can get some work done and even then you're going to wish there was some way to clone yourself because you can't get to all the needs that you see around you.