In the western narrative Soviet dissidents are portrayed as pro-democracy and even pro-market. However literature from the time hints that inequality between the Nomenclatura and the poorer elements of society was seen as an issue.
Even though one can always find different people and motivations, overall, the dissident circle in the USSR was centered around human rights issues, and to a lesser extent, civil rights.
In the later years, this was shaped by the Helsinki Accords, which USSR signed in 1975. An independent Moscow Helsinki Group was formed to monitor USSR's adherence to the Accords. More than ever, they could argue (in courts and otherwise) about illegality of government's actions. "Please respect your own law/Constitution" was a common motto (and remains to this day).
The human/civil rights issues at the centre of attention, such as freedom of speech and religion or 'simply' justice, are more fundamental than the more abstract ideas of 'social justice' or 'democracy'. Democracy, market and such things can be seen as the means to achieve freedoms and justice, and opinions could differ (and still do) about their efficiency towards these goals.
'People on the ground' were mostly busy with more specific problems like defending the accused or disseminating the truth. Many dissidents did not see themselves inherently anti-Soviet and just wanted to live a honest life with dignity, and refused to participate in mass hypocrisy. Unlike the state, they tried to live by the law.
The 'pro-democracy and even pro-market' sentiment can be explained by simple observation that the situation with human rights (etc.) was better in the West, so it would be natural to emulate what they were doing. The inequality and political problems of the West were seen as laughable compared to 'our own', which only reinforced this view.
Also, there was quite universal derision (amongst Soviet dissidents of all kinds) towards the Western USSR sympathisers, who were seen as naive fools (or uninformed useful idiots at best). Given that these sympathisers were nearly always leftists, this creates somewhat incorrect perception that all dissidents were rightists. This is simplification. But it would be fair to say that most dissidents were 'liberal' it its true original sense, which is 'pro-liberty' and hence by extension pro-market.