In order to design a stable regulator, the nature of the output load must be understood. In the old days, when ceramic caps were harder to come by in large capacitances, most regulators relied on tantalum or aluminum electrolytic caps for output filters. These have a moderately high ESR. Accordingly, the regulators were designed to be stable with relatively high ESR output caps. Low ESR caps might not be stable in such old regulators.
When tantalum caps were very difficult to find in the late 90's, a lot of IC makers designed their newer regulators to work with ceramic caps (which have low ESR at high frequencies but not necessarily at line frequencies). Often this was a selling point and may even be mentioned in the datasheet. Over time this became the norm, and still is today. Ceramics are cheap and easy. The only real drawback to ceramic is that if they experience shock, they may produce voltage spikes which can lead to noise. They can be mechanically brittle, also. But very often they are a great, cheap and easy choice.
You can mimic a tantalum cap (for stability purposes) by adding a small resistor in series with a ceramic cap. For example 0.1 Ohm or even 1 Ohm. Just find the ESR of a recommended tantalum cap and use a resistor of that size. Do a stability test when you build the circuit and tweak the resistor value if needed.
As far as ceramic input bypass capacitors go, it is worth reading about the hazards of input voltage overshoot. See Linear Technology App note AN88. It is well worth your time. https://www.analog.com/media/en/technical-documentation/application-notes/an88f.pdf. The quick summary is that the cord from an external power source acts like an inductor. Your ceramic input capacitor in conjunction with this inductor forms a high-Q LC which can overshoot surprisingly high when power is first connected to your board.