auto-sum non-numeric values across multiple tables

Welcome to the forum.
I guess that is doable by combining functions INDIRECT, SUMPRODUCT and COUNTIFS.
If you don't succeed, please post a sample workbook here, as described on yellow banner above.

Added the spreadsheet; thank you. I am new to the forum.

I used your tabs list in the Toc sheet to create a named dynamic range "Tabs" with this formula:

Formula:

=OFFSET(ToC!$C$6,,,COUNTA(ToC!$C$6:$C$1000),1)

Then I use that named range in the indirect countif:

Formula:

=SUMPRODUCT(COUNTIF(INDIRECT("'"&Tabs&"'!B3"),A4))

That formula is for the Race totals. In cell B4 and copied down.
The B3 in the INDIRECT function INDIRECT("'"&Tabs&"'!B3") must be manually changed for the other totals, like this for Ethnicity in B14 and copied down:

Formula:

=SUMPRODUCT(COUNTIF(INDIRECT("'"&Tabs&"'!B4"),A14))

I added a copy of Template tab named Template2 so I could test the formula.
As you add more tabs, they will populate your list and also added to the dynamic named range Tabs I created.

Please check file attached and let us know how it goes.

Good luck!