Trifles shows the ways in which men and women are (stereotypically) conditioned to think and behave in certain ways. This is often referred to as "gender roles." Since these roles are culturally constructed, there is nothing natural or genetic about them. Such stereotypical notions are less stringently enforced and followed today as opposed to the time this play was written and set.
This play is also about the men's obliviousness. The men are looking for hard physical evidence. When either of the women offer a so-called "trifle," the men scoff and deem such evidence to be trivial, something that could not really contribute to the investigation. The psychological approach the women take (something that is now a part of all murder investigations) offers the only real evidence explaining motive. Because the men are so oblivious to the significance of this evidence, they would not have accepted such evidence. Mrs. Hale and Mrs. Peters are well aware of this:
My, it's a good thing the men couldn't hear us. Wouldn't they just laugh! Getting all stirred up over a little thing like a--dead canary. As if that could have anything to do with--with--wouldn't they laugh!
Perhaps another reason Mrs. Hale and Mrs. Peters did not reveal any of their evidence, particularly the dead bird, was out of sympathy for Mrs. Wright. Mrs. Hale notes how John Wright was a difficult man and how tragic the bird's death might have been for Mrs. Wright, "If there'd been years and years of nothing, then a bird to sing to you, it would be awful--still, after the bird was still."
Mrs. Hale also feels guilty that she'd never come to visit Mrs. Wright.
Oh, I wish I'd come over here once in a while! That was a crime! That was a crime! Who's going to punish that?
It's hard to say if they should have turned the evidence in. One could interpret that Mrs. Wright was somewhat justified in killing her husband (if the evidence suggested a long history of mental and/or physical abuse). On the other hand, even if the two women turned in such evidence, the County Attorney and the Sheriff would likely have considered that evidence insignificant. Restraining from turning in the evidence could therefore have been a silent defence of the Mrs. Wrights of the world as well as a reluctant capitulation that their advice on the crime scene would be ignored.
These stereotypes of men's and women's work are obviously not as narrow-minded today as they were during the early part of the 20th century. As a consequence of this loosening up of gender roles and the women's movement in general, there have been more women in positions of authority in all disciplines. Keep in mind that this play was written around 1916: a few years before the 19th Amendment was passed, which prohibits a US citizen from being denied the right to vote based on sex. So, this was a time when women were fighting to be heard: for a political (democratic) voice.