I am not understanding your situation as clearly as most others seem to be, so please bear with me whilst I pose a few questions. By the way, my husband and I are paternal grandparents.
1) Have your partner's parents always behaved like this since your son was born?
2) Do both sets of Grandparents live about the same distance from you, or are one set much nearer?
3) Did your partner ask WHY they didn't like to see photos of your son with your parents?
4) Do both sets of Grandparents enjoy general good health, and are there big differences between the ages of your parents and your partners, as age may not only affect peoples health, but their energy levels, their abilities to cope with young children and/or stressful situations. A big difference in age groups can also mean that generational viewpoints come into play, as in your parents could be early 50's and your partners parents in there mid 80's (unlikely I know, but possible, especially if there is quite a big age gap between you and your partner?).
May I now ask some questions please pertaining to what your answers may be to the above 4 questions? I may also make some observations that are not meant in a negative manner, but may give that impression, if so I am apologizing in advance if that is the case.
Re 1) I asked that because I wonder if, and if so, how much the Covid pandemic may have affected your parents-in-law's current behaviour.
I am still shielding because of rather bad health, and even if I wasn't shielding, my husband and I are both strong believers in following the Covid rules because we care a lot about other vunerable people, and therefore trying our best to not pass the Virus to anyone else in case we are asymptomatic, and therefore didn't realise we had the Virus (of course as I am shielding I don't go out, ever, so my last point was hypothetical).
Therefore, we haven't seen our very beloved and adored Granddaughter since last August, and then socially distanced - we are very sad about that, and not seeing her parents of course too. We gave up on facetiming because it just felt so unnatural sitting facing each other through a screen, and our Granddaughter being made to sit talking to us when she (quite rightly) wanted to go and play! Even by text we haven't had very much to tell each other, as nothing happens, most of the last year has been incredibly boring, and quite depressing.
Re 2). Obviously if your parents live much closer it will be much easier for them to see their son, than for your partner's parents to.
Re 3) To me, this is the biggest issue, why they don't want to see their Grandchild with the other Grandparents. Hopefully that has nothing to do with jealousy (anything that makes our Granddaughter happy, makes us happy too - although in the past we have obviously loved it when we could make our Grandchild happy, and God willing we can do so again in the future.
I am wondering if they didn't like the photo of your son with his other Grandparents because it was taken at a time when they shouldn't have been seeing other because of lockdown rules (because last year during the first lockdown, Grandparents were not allowed to see their Grandchildren unless they all lived under the same roof, at that time they could not be used even for childcare!
Pp's have asked if your parents were in a bubble with you, but at that time if a parent lived with someone else, even their spouse and other Grandparent, you were not allowed to make a bubble - bubbles were for a family and a lone elderly Grandparent, or for a single patent with a child/children, and another supporting household. So IF you were breaking any of those rules, I imagine your parents-in-law may have been very upset, I certainly would have been under those circumstances - but I am not saying that that is what happened with you, only that if it was, or if your PiL thought that was what had happened, then that could have been a reasonable reason to be upset.
My last thought on this is, did your PiL actually say it was the PHOTO of your parents with your son that upset them, could they have meant that they never see your son alone (or with you), that they are only invited when your parents are there too, and that they want a chance to be the only Grandparents there, sometimes, so that they cam build a seperate bond? This is why it was important for your partner to ask his parents why they said that, without that information I don't see how we can offer much helpful advice, or how you and your partner can understand your PiL's behaviour, sorry.
Re 4) The question is hopefully self explanatory.
Good luck going forward OP, and if their behaviour is just down to them not being very caring Grandparents, I don't think there is much more you can do, at least your son has one pair of loving Grandparents.