When using TMUX1511, it is recommended to attach 0.1uF to 10uF De-cap. What are the concerns if I don't utilize a de-cap?
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The de-coupling capacitor is used to help suppress high frequency noise that may be present due to the power supply itself or noise conducted due to the power supply traces. It is used to provide a stable power supply for the IC.
If you do not use the de-coupling capacitor it could cause the power supply to not be as stable and cause unexpected results during operation due to voltage fluctuations and noise on the power supply pin. The bypass cap shunts this noise to ground, so for a more stable multiplexer in the system I'd strongly recommend using the bypass capacitor.