I was building a Bard for a 3.5 campaign and I noticed that online, even in this Q&A it's suggested to swap inspire competence for Song of the Heart as a bonus feat (Eberron Campaign). Now, the inspire competence ability is a prerequisite for the above feat, so I was wondering: do I have to ignore prerequisites for it because it is a bonus feat? And if that's the case, is there an explicit rule for this or something that can support this theory at my DM's eyes?
Eberron Campaign Setting says, on page 34, that
A bard can take these feats [...] as a bonus feat instead of gaining a new form of bardic music at 3rd, 6th, 9th, 12th, 15th, or 18th level.
These bard feats are Haunting Melody, Music of Growth, Music of Making, Song of the Heart, and Soothe the Beast.
This is the basis for people talking about swapping songs for feats in general.
However, Eberron Campaign Setting does not say that this can be done ignoring the prerequisites for those feats, and as you note, Song of the Heart has a prerequisite of inspire competence. I can personally vouch that I had overlooked that until just now—there are doubtless answers on this site where I recommend making this exact swap, and I have absolutely played characters who have done so. I suspect other mentions you find of the idea have also overlooked the prerequisite, because I can find no justification in the rules that would allow you to make that trade otherwise.
That said, I have made that swap on several characters, and it has been to the game’s benefit. Bardic music, particularly inspire courage, are a bit too small to begin with, and don’t provide quite a good enough boost to justify the action costs. You can (and an optimal bard should) mitigate that with Song of the White Raven, and of course you could always take Song of the Heart as a regular feat, but that is basically the crux of my position: characters having feats to play with is a good thing, especially when they use them to differentiate themselves from one another, while feat taxes are a bad thing. Song of the Heart, Song of the White Raven, these are very strong feats, well worth taking normally, but they almost seem then to become mandatory—because inspire courage is a bit anemic without them. Allowing you to get one of these feats as a bonus feat gives another open feat slot “back” to the bard, allowing them to get more creative with it. So I still think it’s worthwhile to consider allowing Song of the Heart to be taken instead of inspire competence, in the context of a 3rd-level bard.