I have not heard of STI being passed by getting ejaculate on the sheets.
I have not heard of STI being passed by sharing underwear but I guess an STI like chlamydia could be passed if there was a lot of fluid and another woman put on the underwear straight away. This could be possible but I have not heard of it happening.
I have not heard of STI being able to migrate through underwear. The only chance of something passing when using rope would be if the rope had any body fluid on it like blood, semen, vaginal fluid and this fluid was able to get directly inside the other persons body e.g. directly exposed to the vagina, broken skin etc.. STI generally do not live for long when they are outside the body given this I have not heard of them passing with what you have described.
Just doing a normal laundry on your underwear and sheets would be enough. No special cleaners or treatment would be needed.
I am unsure of your sexual history but if you are playing with regular partners you could also get everyone tested for STI if you are concerned.
Also have a look at our “Know your chances” web page, it provides information on your chances of getting or passing an STI depending on how you are having sex.
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