If I was going to do a membrane I'd use a fleece backed membrane. I'd never trust a liquid applied membrane on a horizontal surface.
I suppose if the option is no membrane or a liquid applied membrane then maybe I'd opt for the liquid applied membrane.
If you are already tiling the floor then I'd consider an epoxy grout that will effectively make the tile floor water proof.
This sounds like a laundry room that is located on a floor that is not the lowest in the house.
Ultimately if a water hose or the machine breaks in such a way that water is rushing out it won't make much of a difference if the floor has a membrane as the river will flow into other rooms. If there is a slow drip or something the membrane might have some value but generally a washer pan is going to be way more effective for that.
I tend to be over cautious when planning / designing washer spaces on non ground floors. I have done shower pan installation (kerdi) with tiled curb and the washer sits in the shower pan. I don't do that anymore - the traps tends to run dry and it is a lot of work.
My preferred installation method now is:
- Use a waterproof base flooring (concrete or tile).
- Use cellular pvc baseboards ( impervious to water )
- Keep drywall 1/2" or more above floor level or use concrete board / tile backer board.
- Put the washer in a pan
- Use the flood stop washer solenoid valves and put the sensor into the pan near the water hookups.
There are also some sensors now that if they detect water can send you a text message.