Problem:
Allow user to search with date only when there is a date time picker.
Solution:
Actually no it is not possible. The reason is because a datetime custom field and just a date gives 2 different values being stored in the database.
As you may not be away the dates are stored in the database as an epoch or unix timestamp. This means they are stored as numbers and not actual human readable dates.
Take a look at the link below.
https://www.epochconverter.com/
This is a simple converter to clear things up. So a datetime will store the time as well.
Lets say my current datetime is February 14, 2019 9:52 AM, this will convert to 1550155920
While the date only will convert to 1550120400
As you can see both are representative of the same date however the Date only will always default to 12:00 AM as this signals the start of a new date.
So technically speaking it is a Datetime with just a fixed time.
If you look at the comparisons an how they are done, If a user uses date filter for today they will only get posts that have a numeric value equal to "1550120400" even though posts who have values of "1550155920" are still on the same day but because these numeric values are different it will not show up.
