You have to be very skeptical of government statistics on GDP and inflation. They have every motivation to downplay inflation (e.g. let's not count real estate and oil) and play up GDP.
Of course real estate is not included in inflation. Neither is the stock price of Berkshire Hathaway or Amazon. Why should investment goods be included in a price index representing consumer goods?
The cost of housing (owner equivalent rent) is included in CPI, BTW.
This is an area of deliberate misinformation that trips people up. "Inflation" is growth in the money supply. This is why you hear people say things like "washington is cranking up the printing presses" when they talk about inflation.
Whenever you hear someone talk about consumer prices, the CPI, and refer to it as "inflation" you're literally hearing political propaganda being created or repeated.
This is a form of orwellian newspeak that is so common that people will argue about it, because they are certain that inflation is a measure of price increases.
The reason for the newspeak is that it is very easy for government to change the basket of goods, and even to simply exclude important consumer prices from the Index, to make inflation appear less than it is.
You wouldn't claim that nobody uses energy, right? We all use electric power and gasoline in our cars, but these are regularly excluded from CPI because they are quick to reflect the effects of inflation... that is the rise in prices that comes from growth in the money supply.
I know this is tangental to the point you were making, but this misunderstanding of what inflation is causes people to not understand much of the economics in their day to day lives.
The person you were responding to is correct that energy and home costs are generally diminished in CPI to try and make "inflation" look low, and GDP look comparatively better.
Inflation is typically defined as a rise in the general price of goods and services. Growth in the money supply is one possible cause for inflation. If you wish to use an alternate definition, go ahead.
As for your claim that CPI excludes energy and housing, you are simply wrong.
The cost of housing (owner equivalent rent) is included in CPI, BTW.