Is Sheila a socialist?

From the top of my head, no. With Sheila, you must focus on how much more perceiving she and Eric are than the other characters as well as the 'generation gap' - (the idea that the children have conflicting ideas to that of their parents'. It is clearly intended by Priestley for Shiela to become a socialist but, no, there are no explicit quotations. The only way we can even understand that this is what Priestley intends is by looking at the persona of Shiela and some of the things that she says and the way that she says them. She persistently makes bitter and sarcastic comments and is clearly one of the more perceiving characters - besides Eric and the Inspector (although it can be argued that the Inspector wasn't so much perceiving because he already knew he the answers to his questions, hence his 'ghoulish (from Goole) qualities'). This is because she agrees with the Inspector regarding his comments on social responsibility and criticises Birling and the other characters. However, she is seen throught the play to shift blame from herself so there is obviously an element of guilt whithin her and also a little immaturity (seen from her jealousness - although she is definitely not as childish and immature as Eric). So, all in all, she is a little hypocritical and ironic.