Theoretically chlamydia can spread that way. Touching could also lead you to get syphilis and herpes if you touch the typical lesions those infections cause on skin. Gonorrhea is also a possibility.
Obviously, the risk is low compared to oral sex or penetrative sex, but it's not zero. I would recommend you to test as follows:
-Chlamydia and gonorrhea, 3 weeks after the exposure.
-Syphilis, 6 weeks after the exposure, and if you get a negative result, repeat the test 3 months after the exposure, as there are people that take longer to show a positive result.
-Herpes, 3 months after the encounter.
Contacting rectal fluids could also result in an infection with Giardia and other intestinal protozoa that could cause gastroenteritis. Obviously this ones are not STDs but the risk is there, specially if after fingering those people, you put your fingers in your mouth, rectum or genitals.
All the best.