Is 21 days after intercourse for irregular periods accurate for a home pregnancy test?

May be. Depending on the longest interval between your periods. for example if your cycles vary from 21 to 30 days, will suggest you do HPT after 30 days of your last period.
Trust the test. Home pregnancy tests are very accurate. They are the same tests used in a doctors office. They can detect a pregnancy 7-10 days after conception. If you doubt the result you can repeat it in 1-2 days. If you were pregnant the hormone level would rise enough for detection. After this much time clearly you are not pregnant.