Aloha from Hawaii.
We have two Fit Sports (both MT) active in autocrossing
in Street Touring S class of SCCA.
Both using all season street tires so far and gaining in experience.
To be more competitive in class they will have to shod some Extreme Performance summer tires like the Dunlop Z1 Star Spec or Bridgestone Potenza RE-01R or maybe even the R11 when it arrives (depends on sizes available).
Pictures from last event Aug 31.

This 1971 Datsun 240Z ran in B Street Prepared and F Prepared (three drivers). As usual it got Fastest time of the day. The owner has been driving it since 1977 at autocross. It sports custom 15x9 rims with Hoosier A6 275/35-15 tires.

Two SSM Fit Sports cutting through the course.
The competition-

Mazda 6 wagon

Toyota Celica
Results for Aug 31.
STS class
Mazda 6 Wagon 1st of 7 in class, 43rd out of 115 drivers, 23rd on PAX
Toyota Celica 2nd of 7 in class, 81st out of 115, 67th overall on PAX
#58 Fit 6th of 7 in class, 102 out of 115, 99th on PAX (novice event)
#8 Fit 7th of 7 in class, 114 out of 115, 108th on PAX (2nd event)
PAX is with handicap applied for each class.
H stock would be the place for a Fit base or Sport.
By comparison at this event H sport was won by

A 2008 MINI Cooper with Kumho 710 205/50-15 tires
1st of 4 in class, 80th out of 115, 48th on PAX
So even as good as the MINI driver was able to do on R compound tires and with a favorable handicap on PAX. The top STS driver finished higher overall and higher on PAX using Street tires (Extreme Performance Summer tires).
The 2nd place STS Celica driver finished 0.1 sec slower on raw time than the MINI driver but didn't do as well on PAX due to the difference in handicap.
The Fit drivers had to make up 3 to 5 seconds on a 40 second course to catch up to the top 3 drivers in STS class.
And how fast was that 240Z? It finished over 10 seconds faster than the Fits for the event but had every advantage except for modern engineering.
I think once the Fits get some decent tires they will be in the top 3 in class with a little practice. The manual transmissions work fine and both have aftermarket wheels.