I have a birthmark that covers around 1/4 my face - it surrounds one of my eyes, and most of my forehead (it is darker underneath my eye than it is on my forehead). It's not red however, it is brown. It also affects my eyebrow colours (one eyebrow is my natural hair colour, and the other is black). it also affects a patch of hair, which is also black (the hair on top of the black patch covers this, though) - no dye will ever change this hair patch.
However, I also have an olive skin tone, so my mark does blend in better, and it has faded over the years (but it is still noticeable).
As a child, I was called 'Patch', and often asked (as an insult/jibe) who had given me a black eye (in fact, my DH and I were waiting at a bus stop once, and an elderly lady came up to me, glared at my DH, and asked me if I was okay. When I looked very confused, she pointed to my eye, I laughed it off, thanked her, and told her that it was a birthmark - she at least, meant well, unlike others who have used it as an insult).
However, the comments I received? They were from a very small number of people, and the comments weren't that common (I've never been relentlessly bullied due to my mark). I remember discussing it with a friend once, and she said, "Yeah, I noticed it the first time I ever met you. Now, I don't notice it at all, it's just you/your face."
As a teenager, my mum gave me the option to have it lasered (she was willing to take out a loan for it). I thought about it, and declined. Partly because I didn't want her getting into debt for it (but I will also admit that as a selfish teenager that was secondary to my main reason), but mostly because I pointed out to my mum that I wouldn't look like me anymore (in fact, I remember being quite upset that my mum suggested it, as I thought she was implying that I was ugly).
The truth is - I do have a rather large mark on my face, and two different coloured eyebrows, as well as a patch in my hair. But that's always been how I have looked. In the same way, I've always had a left thumb, and nobody is suggesting I remove that either! However, I do understand that it can give others more confidence to remove it etc (people need to make the right decision for them). Similarly, if my mum had decided to remove it for me, as a child, not having it would be part of me too. However, I'm glad this wasn't an option for her (as I believe if it had been available for me on the NHS, she would have done it) - I've got other medical issues that have had been in and out hospitals since childhood, I'm glad that a domestic issue on my face wasn't another thing for me to be in for,