Vlad, your second point was helpful in that I hadn't considered that one of the regular expressions in the XSS Protection configuration href attribute block needed to match the ${/profile/hash} in addition to the rest of the URL preceding and following it. Although to your first point, the RTE actually did save the special characters as-is into the JCR and did not encode them, probably since I was using the source editor mode and not the inline text editor.
What I ended up doing was creating a new regular expression as follows:
<regexp name="onsiteURLWithVariableExpression"
value="(?!\s*javascript(?::|&colon;))(?:(?://(?:(?:(?:(?:\p{L}\p{M}*)|[\p{N}-._~])|(?:%\p{XDigit}\p{XDigit})|(?:[!$&'()*+,;=]))*@)?(?:\[(?:(?:(?:\p{XDigit}{1,4}:){6}(?:(?:\p{XDigit}{1,4}:\p{XDigit}{1,4})|(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])))|(?:::(?:\p{XDigit}{1,4}:){5}(?:(?:\p{XDigit}{1,4}:\p{XDigit}{1,4})|(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])))|(?:(?:\p{XDigit}{1,4}){0,1}::(?:\p{XDigit}{1,4}:){4}(?:(?:\p{XDigit}{1,4}:\p{XDigit}{1,4})|(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])))|(?:(?:(?:\p{XDigit}{1,4}:){0,1}\p{XDigit}{1,4})?::(?:\p{XDigit}{1,4}:){3}(?:(?:\p{XDigit}{1,4}:\p{XDigit}{1,4})|(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])))|(?:(?:(?:\p{XDigit}{1,4}:){0,2}\p{XDigit}{1,4})?::(?:\p{XDigit}{1,4}:){2}(?:(?:\p{XDigit}{1,4}:\p{XDigit}{1,4})|(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])))|(?:(?:(?:\p{XDigit}{1,4}:){0,3}\p{XDigit}{1,4})?::(?:\p{XDigit}{1,4}:){1}(?:(?:\p{XDigit}{1,4}:\p{XDigit}{1,4})|(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])))|(?:(?:(?:\p{XDigit}{1,4}:){0,4}\p{XDigit}{1,4})?::(?:(?:\p{XDigit}{1,4}:\p{XDigit}{1,4})|(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])))|(?:(?:(?:\p{XDigit}{1,4}:){0,5}\p{XDigit}{1,4})?::(?:\p{XDigit}{1,4}))|(?:(?:(?:\p{XDigit}{1,4}:){0,6}\p{XDigit}{1,4})?::))]|(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])\.(?:\p{N}|[\x31-\x39]\p{N}|1\p{N}{2}|2[\x30-\x34]\p{N}|25[\x30-\x35])|(?:(?:(?:\p{L}\p{M}*)|[\p{N}-._~])*|(?:%\p{XDigit}\p{XDigit})*|(?:[!$&'()*+,;=])*))(?::\p{Digit}+)?(?:/|(/(?:(?:\p{L}\p{M}*)|[\p{N}-._~]|%\p{XDigit}\p{XDigit}|[!$&'()*+,;=]|:|@)+/?)*))|(?:/(?:(?:(?:\p{L}\p{M}*)|[\p{N}-._~]|%\p{XDigit}\p{XDigit}|[!$&'()*+,;=]|:|@)+(?:/|(/(?:(?:\p{L}\p{M}*)|[\p{N}-._~]|%\p{XDigit}\p{XDigit}|[!$&'()*+,;=]|:|@)+/?)*))?)|(?:(?:(?:\p{L}\p{M}*)|[\p{N}-._~]|%\p{XDigit}\p{XDigit}|[!$&'()*+,;=]|:|@)+(?:/|(/(?:(?:\p{L}\p{M}*)|[\p{N}-._~]|%\p{XDigit}\p{XDigit}|[!$&'()*+,;=]|:|@)+)*)))?(?:\?(?:(?:\p{L}\p{M}*)|(\$\{(\w|\/|:)+\})|[\p{N}-._~]|%\p{XDigit}\p{XDigit}|[!$&'()*+,;=]|:|@|/|\?)*)?(?:#(?:(?:\p{L}\p{M}*)|[\p{N}-._~]|%\p{XDigit}\p{XDigit}|[!$&'()*+,;=]|:|@|/|\?)*)?"/>
which is just the onsiteURL with my original expressionURLWithSpecialCharacters: (\$\{(\w|\/|:)+\}) value added as a group in the query string parameter section. This enabled AEM to accept this as an href value in my anchor tag.
I appreciate everyone's help!