Why are turbine blades not made out of titanium, only compressor blades?
Titanium is unsuitable because it will react with oxygen and carbon at high temperature, well below its melting point, making it very hard and brittle. Welding titanium is very complicated because it needs to be shielded extremely well from any oxygen when hot. Ti$_3$O will form above 500°C, and Ti$_2$O above 600°C.

Initially turbine blades were made of steel alloys, but they have been displaced by nickel alloys.

Also, they operate in an environment which requires constant cooling, so they can be 200 - 300°C cooler than the turbine entry temperature of the gas coming from the combustor(s). Modern turbine blades are hollow and have a perforation at their leading edge. Pressurized, relatively cool air is forced through the blades and the perforation and flows around the blade's surface, creating a cool sheet of air to shield the blade from the hot gas. Also, before entering the turbine the gas is accelerated, which already lowers its temperature. See the plot below of parameters inside an older engine taken from this source.



Shortly past the fuel injectors the maximum gas temperature of approx. 1800°C is reached, which drops to 1100°C at the entry to the first turbine stage. Note that this temperature has been raised to 1500°C in modern military engines! At the same time, the highest temperature is connected with the lowest speed (30 m/s), and the flow accelerates to 200 m/s directly before entering the first turbine stage.

Titanium in contact with oxygen would lose a lot of its strength at these temperatures, even though its melting point is at 1650°C.