I am not even sure what that means - in what way are they responsible for the high cost of living? I think he meant because they participate in the workforce at lower percentages than general society. presumably, if the Haredi community would participate equally like everyone else, the government would be able to lower taxes as the tax base of people paying in would be greater.

I think that is bunk. The government is not going to lower taxes because some more people are paying in. I dont know who he thinks he is fooling. The high tax on gas is not because fewer Haredim are working. The high tax on sugary drinks is not because fewer Haredim are working. The level of arnona and income tax and VAT and all the various business taxes for people who own businesses, and all the other taxes are not coming down if more people start working. The graph of cars being purchased in Israel does nothing but go up yet the tax on gas or on cars has not gone down even a bit let alone commensurately.

Besides for taxes and the workforce, the Haredim are experts in cheap purchasing. They buy in bulk, they use community forces and group purchasing power to attain lower costs. Besides for homes, they often do not even purchase higher priced items. 

Haredim suffer from cost of living increase as much as anyone else, but the cost of living has always been high in Israel and it isnt the fault of any one specific group (other than maybe government people).