YECS need changing decay rates, to discard radiometric dating results that prove them wrong. They also like the fine tuning argument. They don't think about consistency. The arguments are useful to them therefore they are both good.
This is what I am really interested in. I don't see how one can honestly use both claims. Maybe one or the other.
To clarify a bit: Phenomena like radioactive decay and the speed of light are tightly connected to the fundamental physical constants, so one cannot vary the phenomena without messing up the constants.
As NosyNed pointed out, the fine tuning argument is probably overstated. I wonder if one could "turn the tuning knobs" to get from one set of useable fundamental constant values to another set without passing through life-hostile conditions, and whether life formed under one set could survive under another.