Hudson, who is nearly two months old, has the heart disease cardiomyopathy, desperately needs a heart transplant to survive.
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Father Kevin Bond posted the photo to a Facebook page called 'Hudson's Heart' to raise awareness and money for medical costs.
But, when Kevin tried to advertise the page, Facebook bosses rejected the post, citing the photo as being too "scary, gory or sensational" for the site.
The heartless response left the father angry and upset, causing him to write on his Facebook page: "What is offensive about this picture of my Son?
"In Classic Facebook fashion the link they provided to appeal this decision doesn't work, and all efforts to contact them have failed.
"Facebook you should be ashamed of yourself.
"Of all the garbage you endlessly pedal over the Internet, a picture of my Son is where you draw the line? Disgusting."
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Post by Hudson's Heart.
Unsurprisingly, people were outraged.
One wrote: "I can only assume a computer made this decision. No human could think otherwise."
Another added: "I am so sorry to read this. I couldn't imagine someone putting that sweet child in the category they did. Prayers for you and sweet baby."
Since the outcry, Facebook have released a statement apologising for their decision.
It read: "This was a mistake on our part, and the ad has been re-approved. We apologise for any inconvenience this caused the family."
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The social media bosses, however, failed to apologise to the Bond family directly - something which Kevin has slammed them for.
He said: "I read Facebook's response on media outlets last night. They apologised for the inconvenience this caused my family.
"Inconvenience was never an issue. Having my beautiful son compared to dismembered bodies, vampires, zombies, etc hurt me, and my family."
Earlier this week Facebook refused to remove a video of a kitten allegedly being doused in petrol and set on fire because the footage does not breach any of the social network's rules.
More than 14,000 users have commented on the clip - many expressing their disgust - but despite complaints, Facebook have not removed the two minute film.
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