JOEL - I have never heard anyone tell a woman that they are "prohibited" from attending a priesthood meeting. I have searched the main Church Handbook and see nothing that says this. If that has happened then the person who told them that is misinformed. Women don't attend because the subjects spoken of are geared toward males who hold the priesthood in support of their fatherly, spousal, and priesthood duties. The only thing women are "prohibited" from is in the actual performance of priesthood ordinances(baptizing, administering the Sacrament, etc.). If a woman really wants to sit in on a priesthood meeting to see what goes on, I don't know of any Bishop who would deny her that. I just don't know of many women who would really want to do that(nor any man who would want to attend Relief Society). Some male leaders only occaisionly attend Relief Society meetings and functions because the Relief Society is supposed to be under the direction of the Bishop or Stake leader, who's priesthood responsibility is to oversee everything that happens in a ward or Stake. That's the way God chose to run His church. Other than that, the women have their own leaders who are in charge of everything in their organization and who receive inspiration from God in performing their leadership functions.

DIANE - Why are non-member visiting males permitted to attend Sunday priesthood meetings when most don't even have a fractional-knowledge of the LDS gospel/practices?

JOEL - The same reason why non-member visiting females attend Relief Society meeting. I think it's because the men would probably feel more comfortable with the men in the priesthood meeting instead of being the only male sitting in a Relief Society meeting. Perhaps also to help them obtain a "fractional-knowledge of the LDS gospel/practices" as it relates to the men.

DIANE - What is the rationale for this (perceived) "secrecy" and what actually takes place in these "gender-exclusive" meetings that females must be excluded from? What information could possibly be shared - either via our Heavenly Father or from mortal decision makers - that all adult church members should not be privy to at the same time?

JOEL - It is only "perceived secrecy" by those outside the church and perhaps some members who don't understand how it is supposed to work. In my experience the men don't hear about anything any sooner than the women do, except perhaps at the higher levels of church government(it has to start somewhere). In every monthly Bishop's or Stake President's leadership meetings, leadership representatives from both the male and female organizations are there finding out the same things at the same time. They then relate the same relevant information to the male and female members at the same time.
There is nothing "secretive" going on in either the Priesthood meetings or the womens' Relief Society meetings. In fact both organizations teach their weekly Sunday lessons from the same manual. And a couple of times a year both the men and the women meet together to be instructed by the ward or stake leaders. Besides this, men learn of their God-given roles in priesthood meeting and women learn of their God-given roles in Relief Society.
In the leadership meetings both men and women leaders learn of things that are helpful in running the church programs and providing service to the ward members. That's the only thing that happens in those meetings and its the only thing that happens in the few male-only leadership meetings at the higher levels.

DIANE - I am concerned that overt biases such as this often have the potential to perpetuate inequality between the sexes and the potential for oppressive abuses through a male sense of entitlement and an uneven playing field.

Joel - If women are truly getting this impression then both they and the men are not understanding nor conducting themselves according to what God has told them regarding the male and female roles and priesthood authority:

From the Bible:
"Nevertheless neither is the man without the woman, neither the woman without the man, in the Lord." (1 Cor. 11: 11)

From the "Proclamation on the Family":
"By devine design, fathers are to preside over their families in love and righteousness and are responsible to provide the necessities of life and protection for their families. Mothers are primarily responsible for the nurture of their children. In these sacred responsibilities, fathers and mothers are obligated to help one another as equal partners." (Proclamation on the Family, 1995)

From the Doctrine and Covenants:
"That the rights of the priesthood are inseparably connected with the powers of heaven, and that the powers of heaven cannot be controled nor handled only upon the principles of righteousness.
That they may be confered upon us is true; but when we undertake to cover our sins, or to gratify our pride, our vain ambition, or to exercize control or dominion or compulsion upon the souls of the children of men, in any degree of unrighteousness, behold, the heavens withdraw themselves; the Spirit of the Lord is grieved; and when it is withdrawn, Amen to the priesthood or authority of that man.
No power or influence can or ought to be maintained by virtue of the priesthood, only by persuasion, by long-suffering, by gentleness and meekness, and by love unfeigned:" (See D&C 121:35-46)

DIANE - Through our gift of individual free-agency there are many LDS women who actually live a more worthy life than many fellow male members, yet are being relegated to second-hand information and an expectation of submissive status through expected reverence to a (conveniently all male) priesthood authority.

Joel - In fact there are probably more "worthy" females than males in the church, but as I stated above the women do not get information second-hand compared to the general population of male members. The only level where this really happens is with the highest authorities of the church(prophets) who get it directly from God. Everyone (both male and female church members) gets that information second-hand. But second-hand does not mean it is incomplete nor incorrect information. If the men are conducting themselves as directed in the scriptures(D&C 121), women should not feel they are at a "submissive status".
I am not sure what else to tell you. God is the one who set up His church with a male-only priesthood government. Any changes to this will have to come directly from Him.