Why do people insist upon making clear lines of demarcation when introducing family members?
I hear it a lot. "This is my step-daughter", or "That's their adopted son", even, "The older two are his from a previous relationship". Are the circumstances of the child's birth pertinent to the child's identity? Do they somehow alter or inform a person's character?

If that's the case, why do we never (or rarely), hear anyone introduced as, "So-and-so's bastard child"?

These lines of demarcation, while potentially helpful to a genealogist, in polite conversation do nothing but mischaracterize the relationship.
Is a parent more or less a parent based on step- or adoption status? If not, then why make a point of pointing it out? Is the child more or less loved, based on that status?

It often happens when introductions are being made by someone outside the family. It's an awkwardness only because it is highlighted. Sometimes family members make the distinction themselves from the start, just to stave off intrusive questions. Ant is questions posited are at best impertinent, and at worst, ill mannered and rude. If asked, they ought to be treated as such. There's no need to forestall them. Believe it or not, they likely occur to people much less frequently than one might think.

On a similar note, when Mother's day or Father's day are celebrated, why would we hear praise and recognition for the honored individuals, with the follow-up, "and you step-parents and adoptive parents too"? It's demeaning. It's like saying, "lunch is served, everyone may line up at the buffet, and you black people can eat too." As if that's acceptable.
As a society, we have enough to divide us. As a stepchild and an adoptive parent to children of another race, I can attest that non-traditional families have unique hurdles. Having such non-essential trivia pointed out adds nothing to the discussion.
Blended families and adoptive families have something traditional families never do. At some point people made conscious and binding decisions to love and accept "someone else's kid(s)" as their own, and children have decided to love, trust, and accept as parents people who are new to them. In many cases they endure physical, financial, emotional, and spiritual hardships that traditional families cannot understand. Those children who find themselves in such a family learn to make adjustments and to fit together as a family with varying degrees of success.
To make the unnecessary distinction is to mark non-traditional families as something "other", "foreign", and perhaps, positionally "less" than traditional families, often making those transitions more difficult.
Note that throughout this essay, the dichotomy is between "traditional" and "non-traditional" families, versus the common distinctive offered between, "natural" and "blended", or "other" types. That's a conscious decision. There's nothing unnatural about people loving other people and forming a family. I'd call that "supernatural".