It's a good question about FIT bowel cancer tests when you may have visible bleeding.
To be specific, FIT tests for blood inside the sample. With bleeding from haemorrhoids and other conditions very near the anus - like a fissure-in-ano - most of the bleeding actually happens after the stool has passed and it's the minor trauma of passing the stool that causes the haemorrhoids or fissure to bleed. People will often see blood on the paper but the stool actually won’t have blood in it. Even if haemorrhoids or fissures do put some blood on the stool, it's often only in a certain part of the stool, just adjacent to where the haemorrhoid or fissure actually contacts the stool. If you sample from a different area of the stool, it's easy not to have blood inside the sample.
But does the above compromise the ability of the FIT test to pick up bleeding from bowel cancer? The answer is, no. Bleeding from cancer isn't so much due to the trauma of the passing stool, it's a constant thing: drip, drip drip… into the inside of the bowel where the stool is then mixed up. So blood from a cancer is generally present throughout the stool.
Studies have actually shown that in people who complain of rectal bleeding around 2/3 will have a negative FIT and in those people, their risk of bowel cancer was the same as for people who didn't complain of bleeding and had a negative FIT (about 1 in 1000). Here's the study if you want to know more https://pubmed.ncbi.nlm.nih.gov/33605522/.
The upshot is this: if you do a FIT test and it's negative then you can be reassured that it's very unlikely that you have bowel cancer. If you do a FIT test and it's positive and you know you have haemorrhoids which bleed then it's possible that the positive result is caused by haemorrhoids. But bear in mind that haemorrhoids are very common and it's perfectly possible to have haemorrhoids and bowel cancer. So we wouldn't say for sure that a positive FIT is caused by haemorrhoids just because you have them - it's best to do a camera test to be sure.
If you're looking to see if you have bowel cancer, a FIT test is still a good first investigation even if you have some bleeding sometimes.
We also have an article here that explains more about the FIT test that may be helpful: https://www.selph.co.uk/learn/fit-tests-for-bowel-cancer-what-you-need-to-know.