I completely agree with you if that was the situation.

I am not suggesting that anything be removed, just fixed.

This means the search box is available on the https login page,
The customer conducts their search without getting a warning message
The sale is made (hopefully).

However, scenario number 2...
The customer goes to login but thinks "hmmm, I wonder if they sell green blankets in the store?".
The search box is there so they type in "green blankets" but get a security warning message.
This makes them think "not too sure about this... why am I being warned? maybe I shouldn't shop here if the store is not secure?"

Get my drift... ?