Using COUNTIF with VLOOKUP to return # of results for a given date

Hi folks!

I'm working on creating a client tracking sheet which tracks some metrics for drop-in clients who are coming in at a given date. So far my SUMIF function seems to be working, pulling number of services given on a specific date, but since each of these are separate columns which effectively just have to be ticked per visit, it seems that a similar format isn't working for a different issue: I'm trying to count number of clients who have the same trait (in this case, race), and return a value of # of clients who belong to that demographic. Below is my current Formula I'm using:

=COUNTIFS('Input Data'!J:J,VLOOKUP(A2,InputData,10,FALSE),="Latinx")

So the idea is that in the "Race" column there are different values: Black or AA, White, Latinx, Asian etc. On the output calculator I am trying to get it to read that column and return all people who have "Latinx" marked as their race, then I would have other columns for the other races that would use a similar format. I feel like it should be straightforward, but for some reason I can't get my head around it. Any advice?

In the attached file, the formula should return 2 Latinx clients.

Thanks!
Parker