Can Stanley be regarded with any sympathy?
It's really difficult to draw any particular sympathy for Stanley. He is intensely base in terms of how he approaches reality. For Stanley, consciousness is defined by his ability to take what he wants and to assert his power in a form of emotional and physical control. In this, Stanley is really difficult to find sympathetic. If one were to take a larger psychological point of view, perhaps there is something in Stanley's background that made him the way he is today. This would be something that could bring out sympathy in that something in Stanley's background helped to create him in the way he is presented. However, I am not sure that this is Williams' intent in his characterization:
In earlier versions of the play, Stanley had a gentler, ineffectual side, but in the final writing of Streetcar Williams made him Blanche's complete opposite—angry, animalistic, and reliant on his basest instincts.
In the end, this is where it becomes a challenge to find sympathy in Stanley.
Yes. His life with his wife has been worsening ever since Blanche has stepped in his house. She acts like a parasite that threatens the marriage of Stanley and Stella's while reminding constantly to the latter how their lives were at Belle Reve. Further, Stanley is a down-to-earth man who was very happy with his wife before the arrival of Blanche and due to them living in a closed space, Stanley and Stella do not get to satisfy their carnal desires as they used to do. Actually, Williams concentrates more on the plight of Blance and thus, it becomes difficult to sympathise with Stanley who is often described as being the new South emerging to destroy the old one in the person of Blanche.
It should also be noted that on the night that Stanley's son were to be born, he tells Blanche if she wants to bury the hatchet, but Blanche blatantly refuses. Somewhere, it is in great part Blanche who is the one who should be less pitied, given her promiscuity and high pretensions about being a woman of 'old-fashioned ideals' when she even goes to the extent of inducing her student to engage in coitus with her. As for Stanley, he is surely a survivor of the Stone Age but it is this bestial quality in him that Stella yearns for as the latter tells that she nearly goes wild when Stanley is away.
an everyman pushed to extreme lengths to protect his family.