As the title says, can you use the features this feat grants despite not being proficient in shields?
Rules as Written answers, provide sources please.
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PH170, the feat in question, says "[y]ou gain the following benefits while you are wielding a shield". The feat says nothing about wielding a shield you are proficient in—otherwise it would be on the prerequisite line—just that you have to wield a shield.
Of course, if you're not proficient with the shield, many of the benefits are moot.
While adding your shield's bonus to Dex saves and gaining the ability to take no damage from a successful Dex save those saves are going to be harder to succeed at with disadvantage.
Armor Proficiency. Anyone can put on a suit of armor or strap a shield to an arm. Only those proficient in the armor's use know how to wear it effectively, however. Your class gives you proficiency with certain types of armor. If you wear armor that you lack proficiency with, you have disadvantage on any ability check, saving throw, or attack roll that involves Strength or Dexterity, and you can't cast spells.
Therefore, not being proficient with a shield grants disadvantage on Dex saves—the same saves the shield master feat is meant to improve.