Common grounds and differences between conservatives and socialists for funded subsidies

Are taxpayer funded subsidies for child and elder care policies on which conservatives and socialists might find some common ground? Why might a conservative favor them? Why might a conservative oppose them? At the end of the day, do you think conservatives and socialists might come together in this issue space or do you think they are destined to remain at loggerheads as they were for much of the 20th century?