That's what the article Restricting Activities of Transgender Church Member | Ask Our Experts | Church Safety says, in effect.
Chromosomes are the structures on which the genes are carried, which, in turn, are the mechanism by which hereditary characteristics are transmitted from parents to off-spring. An individual normally has 23 pairs of chromosomes in his or her body cells; one of each pair being derived from each parent. One pair of chromosomes is known to determine an individual's sex. The biological sexual constitution of an individual is fixed at birth (at the latest), and cannot be changed, either by the natural development of organs of the opposite sex, or by medical or surgical means. As a result, a sex change operation cannot affect a person's true sex.
Taking things one at a time:
One pair of chromosomes is known to determine an individual's sex.
Counterexample: J Clin Endocrinol Metab. 2008 Jan;93(1):182-9
A 46,XY mother who developed as a normal woman underwent spontaneous puberty, reached menarche, menstruated regularly, experienced two unassisted pregnancies, and gave birth to a 46,XY daughter with complete gonadal dysgenesis.
The biological sexual constitution of an individual is fixed at birth (at the latest)
Counterexamples : Bone marrow-derived cells from male donors can compose endometrial glands in female transplant recipients by Ikoma et al in Am J Obstet Gynecol. 2009 Dec;201(6):608.e1-8 & Transplanted human bone marrow cells generate new brain cells by Crain BJ, Tran SD, Mezey E. in J Neurol Sci. 2005 Jun 15;233(1-2):121-3 :
These show that a bone-marrow transplant recipient's entire bodies gradually become genetically identical to that of the donor due to cell turnover. Even the brain. Even the reproductive glands.
The biological sexual constitution of an individual... cannot be changed... by the natural development of organs of the opposite sex
Counterexample : Imperato-McGinley J, Guerrero L, Gautier T, Peterson RE. Steroid 5alpha-reductase deficiency in man: an inherited form of male pseudohermaphroditism. Science 1974 Dec 27; 186 (4170): 1213-5
In an isolated village of the southwestern Dominican Republic, 2% of the live births were in the 1970's, guevedoces (actually male pseudohermaphrodites). These children appeared to be girls at birth, but at puberty these 'girls' sprout muscles, testes, and a penis. For the rest of their lives they are men in nearly all respects. Their underlying pathology was found to be a deficiency of the enzyme, 5-alpha Reductase.
The original question:
A man who has surgically changed his gender to a woman is active in our women's ministry activities. Church leaders are increasingly uncomfortable with this arrangement because most of the women in the church are not aware of this person's true gender. Could we be exposed to legal risk by restricting—or even excluding—this person from women's ministry activities?
"This person makes us feel uncomfortable - can we safely shun and exclude them"? The "Church Leaders", not the congregation, are looking for an excuse. A perfect example of Lack of Charity.
1 Corinthians 13:2
2 And though I have the gift of prophecy, and understand all mysteries, and all knowledge; and though I have all faith, so that I could remove mountains, and have not charity, I am nothing.