We so far have a sample size of 1. We know that a largish star, with a surface temperature at about 4.5 billion years of 5800K can be stable enough to support life for long enough for intelligence to evolve. We are fairly sure that very large stars don't last long enough.
With only one data point to extrapolate there is a tendency to think that stars that are like the sun offer the best environment for life. We are fairly sure that very large stars don't last long enough. It seems reasonable to exclude highly variable stars, or ones whose outbursts would strip the atmosphere from any planet. Intuitively these would seem to be less likely sites for life. But there is no strong evidence in the form of multiple discoveries of extra-terrestrial life to support this.
In short we don't know what stars can support life.