However, I've seen controversy on lemmy.world's bot with this

TBH, I think you'd get the same controversy no matter what bias / fact checker you integrate. I've had MBFC embedded for close to a year now, and while I won't say it's perfect, the consistent "controversy" common to it and lemmy.world's bot is blown widely out of proportion and basically boils down to people getting upset about:

1. Their favorite rag that tells them what they want to hear is deemed low credibility or heavily biased.
2. Not understanding that the ratings are determined over a significant period of time (e.g. recent geopolitical events or ownership changes may not be factored in yet)
3. Personal disagreements with the given bias/credibility rating (which often overlaps with numbers 1 & 2 above)
4. Hyper-focusing on the "bias" aspect (and screaming it's US biased) rather than overall credibility ratings. FWIW, I've looked into MBFC's bias criteria, and they're transparent about their scoring. Obviously, "left/right" is a spectrum viewed through your local Overton window, but MBFC does a pretty decent job of filtering it to lowest common denominator criteria.
5. The tin-foil hatters and "don't fact check me, bro!" crowds doing what they do.

Having already blazed this trail, my advice is, if you have more than one source and it's practical, add both for extra coverage and make it optional so the people who would shriek about it can just turn it off.

The whole website bias rating is flawed by design. Each publication have multiple authors, which have different inherent biases and personal leanings that even unconsciously can influence the writing. And while corporate influence does exist and politics are unavoidable, labelling everything a site published based on a small dataset just makes the situation worse.

I was afraid that Photon will go the same route as Tesseract (originally fork of Photon) who went all into in flawed media bias checking and ruin the good project, but having the button for people that care about it is a good compromise.

As far as MBFC specifically, https://slrpnk.net/comment/10200142 highlights the issues with it quite well.

https://spinscore.io is a relatively new tool, but shows some promising results so far.