My comment about being "being vital" was more to point out that it's clear the FB page is more important TO HIM, but your page is not , to you. That's why he is making a big deal out of this and putting pressure on you, whereas you are not as persistent about it. Vital. Significant. Critical. It's semantics really. The point is it's more important to him to have many LIKES on FB but it's not to you. You explain a lot about how he sees his page being used as part of his business plan, and how you use yours. But then you say the point is that you don't want to LIKE a page if you don't LIKE the business. So why bother comparing him and you at all? By doing so you are, in a way, creating background that is relevant to the story.
So if the issue is that you simply don't want to like his page then don't. My original answer still stands. I think it's a minor issue to just LIKE it and then ignore it. I think everyone uses FB diffferently and LIKING a page you don't truly like is not going to impact you in any tangible way so why cause a rift in the family over it? If his posts on your jewelry pictures are irrelevant then delete them. It's your page, and you manage it the way you want. (Though I see the same posts on Entenmann's Cake FB page and they never delete any Oooooh or Aaaaahs and they seem harmless enough.) I think you need to ask yourself if your opinion of him is tainting your thoughts here. If someone else, a stranger even, made the same post would you be so quick to assume it's meant sarcastically?
Now you bring up other issues about BIL and boundaries so really this sounds like a BIL issue not a FB LIKE issue. You sound like you just don't want anything to do with him. So UNlike his page, and unfriend him from your jewelry page. If you're backed into a corner then shine up your spine and tell the truth. That you use FB in a different way than he does and reversed the LIKES because you didn't find them relevant to your interests. He sounds like a pest, so if your honesty offends him and he backs off, it's win-win.