Replies

If you have the urge to have sex, in the bonds of marriage, but do not do so, is that immoral too?
Yes.  St. Paul, the Apostle, clearly asserts this in his first letter to the Church at Corinth, wherein he wrote:
3 Let the husband render unto the wife due benevolence: and likewise also the wife unto the husband.
4 The wife hath not power of her own body, but the husband: and likewise also the husband hath not power of his own body, but the wife.
5 Defraud ye not one the other, except it be with consent for a time, that ye may give yourselves to fasting and prayer;
I Corinthians 7:3-5a KJV

Is it immoral not to be married in the first place, never to have children?
There are two separate questions, here.  Answering the second, regarding children, per my previous post [14]; I think scripture is fairly clear that, while it is not immoral not to have children (perhaps due to infertility, etc), it is immoral to try not to have children.  The first, regarding celibacy, ties into your next question, so I'll deal with it below.

Some faiths do not allow their clergy to marry. Is this not denying God?
No.  Jesus had this to say about chosing celibacy:
10 His disciples say unto him, If the case of the man be so with his wife, it is not good to marry.
11 But he said unto them, All men cannot receive this saying, save they to whom it is given.
12 For there are some eunuchs, which were so born from their mother's womb: and there are some eunuchs, which were made eunuchs of men: and there be eunuchs, which have made themselves eunuchs for the kingdom of heaven's sake. He that is able to receive it, let him receive it.
Matthew 19:10-12 KJV

Note that Jesus clearly states that this endorsement of celibacy is not universal, but that those who are able to accept it should do so.  Also, let the reader not be distracted at Jesus' placing the discussion in terms of eunuchs, as such were quite common in that day and all would readily grasp the broader implication of his discourse as it relates to them that are not eunuchs.  That is, if those who are not eunuchs can accept it, they do well to live as though they were He that is able to receive it, let him receive it.

The Apostle Paul addresses the matter of celibacy in this way:
32 But I wish you to be without care. The unmarried cares for the things of the Lord, how he shall please the Lord;
33 but he that has married cares for the things of the world, how he shall please his wife.
34 There is a difference between the wife and the virgin. The unmarried cares for the things of the Lord, that she may be holy both in body and spirit; but she that has married cares for the things of the world, how she shall please her husband.
35 But I say this for your own profit; not that I may set a snare before you, but for what [is] seemly, and waiting on the Lord without distraction.
36 But if any one think that he behaves unseemly to his virginity, if he be beyond the flower of his age, and so it must be, let him do what he will, he does not sin: let them marry.
37 But he who stands firm in his heart, having no need, but has authority over his own will, and has judged this in his heart to keep his own virginity, he does well.
38 So that he that marries himself does well; and he that does not marry does better.
1 Corinthians 7:32-38 Darby (Public Domain)

Barring the clergy from marriage simply imposes that only those who are able to accept celibacy should pursue the ministerial calling.  This is no denial of God, but only a reinforcement that those whom God calls to remain celibate are more free to focus upon the things that please God, and that such is a preferable quality for one in clerical ministry.  So, this does not deprive the priest of a happy marriage rather it reaffirms that he ought have been of a settled mind regarding celibacy before.  In fact, I would frame it in this way: no man ought to pursue clerical office in any denomination barring clergy from marriage unless that man is wholly committed to celibacy from the outset; being at peace with the issue and having fully laid it to rest in his own heart and mind.

One can go on and on along these lines of thought.
Yes, and I really think that the issues are worth discussion, because many perceptions about them are fairly easily affirmed or refuted in scripture.  So I think this exploration is healthy.  Ultimately, however, there is no substitute for personal study of the Bible, for which I strongly recommend a tried-and-true two-step approach: open book, insert face.

So, I think it is a distinct moral difference that is something worth patting oneself on the back over.
Don't get me wrong; I did not mean to imply that there was no moral distinction; there is.  But the difference is not between immoral and moral, but between immoral and less immoral.  Since less immoral is still immoral, if we engage in patting ourselves on the back, let us do it with sobriety, as those who recognize that, while we have done well, we could have done better.