Check If Post Was Published More Than 6 Months Ago Using get_the_date

The problem is that your date format is not a standard format that strtotime() understands. Instead just use get_the_date() with the format set to 'U', which returns the timestamp, and compare that to strtotime( '-1 year' ):

if ( get_the_date( 'U' ) < strtotime( '-1 year' ) ) {

}