No, as these features make no mention of changing the proficiency requirement.
5th Edition uses a “specific beats general” rule. Here’s an excerpt from the rulean excerpt from the rule as summarized in Xanathar’s Guide to Everything (p. 5):
[...] a general rule is in effect as long as something in the game doesn’t explicitly say otherwise.
This means that for a rule to create an exception to another rule, it must do so explicitly.
Since Subtle Spell and Aberrant Psionics make no mention of shield and armor proficiencies at all, they do not interact with them in any way. Therefore, to cast spells while wearing armor or a shield, you must be proficient, even with Subtle Spell or Aberrant Psionics.