Thanks for writing.
It’s a really good idea to wash your hands with soap and water in between fingering partners. The sexual fluids from one person can stay on your hands (even if you wipe them off) and be transferred the other person. Sexual fluids can carry STIs like HIV, Gonorrhea, and Chlamydia and those can be passed if your hands are not washed between partners. Another alternative is getting disposable gloves to use, and switching gloves between partners.
For oral sex it’s less likely to pass sexual fluids. Brushing your teeth or using mouthwash could potentially reduce the chance of passing the STIs transmitted through sex fluids, but the chance is already low. Some STIs are passed by direct skin-to-skin contact and can be passed from your mouth to another person’s genitals. The STIs passed through skin-to-skin contact are Syphilis, Herpes, and HPV. You can reduce the chance of passing these if you use a barrier with your partners… for example when giving oral sex to a woman you can use a dental dam over the vulva/vagina.
Hope this helps!
Please feel free to submit another question as needed.