Rising rates usually affect home prices to some extent. This was evident in the most recent boom when affordability was up in the 140% range, rates were low and there was a climate of optimism. Buyers paid increasingly higher prices for properties.
Another example is in the early 80's when rates were high topping out at 17.5% prices were discounted to keep monthly obligations and affordability where buyers could afford to buy. Having said this, today's circumstances contradict past actions. Affordability is up in spite of historically low rates and prices are down at the same time. Usually prices would be up as rates go down but that is not happening.
Consumer confidence and the adverse effect of short sales and foreclosures have kept prices down while rates are down. Additionally, should interest rates increase as they may, will depend on the economy, and how deep the correction in property values goes. Also how optimistic the future looks to the consumer will impact how interest rates affect the future of home prices.
Also employment, inflation and wages will play an important role. When we look at the past 20 years we have had rates as high as 13% and as low as 4.5% and overall home values have continued to increase. In the short term you can be up or down but in the longer term if you are in a property over 7 years you usually are making money in addition to the fact you have had shelter. We don't look at it this way but if a $400,000 property cost you 7% in acquision costs $28,000 and over 7 years it grew 7% you would get 100% return on your original investment plus any tax benefit you would enjoy, plus shelter.
The ability to control $400,000 with 7% is still hard to beat. (Example with FHA it is a 3.5% down payment plus closing costs) I'm not an economist but I believe real estate is a good investment. If inflation is in our future real estate usually will track pretty closely to the rate of inflation. I am including a historical rate chart with this post I believe it supports my position that over time property values grow.