Formula is currently double-counting a cell

I've got the following formula that looks for certain keywords in cells within a column.

=SUMPRODUCT(COUNTIFS('Data'!$G:$G,{"*" & Settings!$E$5 & "*","*" & Settings!$E$6 & "*","*" & Settings!$E$7 & "*"}))

Here is an example of the data on the Data sheet.

And the settings sheet.

Using the above formula I get a count of occurrences for each of the months in the quarter. So I would get a count of 8. Instead, I need the count of cells that contains at least one of these months in the quarter. So the answer should be 4.

How can I achieve the count of cells that contain at least one of these months?

Edit: for the sake of simplicity I have trimmed this formula down to the problem area. I am using countifs as opposed to countif because I have other conditions that need to be met.

You may try (going with an assumption those'll are plain text formatted):

=countif(index(regexmatch(Data!G:G,join("|",Settings!E5:E7))),true)