Regex to test if string begins with http:// or https://

Your use of [] is incorrect — note that [] denotes a character class and will therefore only ever match one character. The expression [(http)(https)] translates to “match a (, an h, a t, a t, a p, a ), or an s.” (Duplicate characters are ignored.)

Try this:

^https?://

If you really want to use alternation, use this syntax instead:

^(http|https)://