The workers (and thus the unions) were opposing government policies that were hurting them. Funnily enough (though unsurprisingly), strike rates as well as union membership fell under Thatcher because of her union reforms (which removed much of their bargaining power) -- and so the commonly held view of daily strikes in the 1980s (something Yes Minister capitalises on) isn't really an accurate portrayal.
By laying criticism on one and not the other, Yes Minister showed their Thatcher bias. And it's not at all a stretch to say they had a Thatcher bias -- Thatcher herself said that Yes Minister was her favourite show. So while Yes Minister was very heavily critical of the civil service, they weren't fundamentally critical of the views of the government. Thatcher was very strong on civil service reform too.