Largely because those are inelastic goods, they are always purchased. While some may be able pull back, most cannot.
Higher interest rates for loans for larger purchases or business purchases/investments certainly are impacted by higher rates.
The answer, directly from the Fed is, "No, our interest rate hikes will not change the price of gas at the pump or the cost of eggs."
As I mentioned, things like houses are complicated, clearly there has been a _bit_ of downward pressure, but there are a ton of supply side complications preventing a big change (building has slowed, people with low interest rates are holding etc).