1. There are a lot of other concerns beyond what you mentioned. Noise, heat, pollution, destruction of neighborhoods...
Noise is largely due to gas turbines or diesel generators running. That's again the sort of thing where reasonable regulation can help out. Some other noise claims are also just not plausible; there have been examples of noise complaints about completed data centers which hadn't been turned on yet for example. The heat claims are generally not plausible. If you take the claims seriously, they'd have to be generating far more energy than they are. Meanwhile, people don't object to large parking lots which are constantly taking in sunlight and converting to heat. I'm also not sure how they engage in "destruction of neighborhoods" any more than any other building project.
2. None of the problems either of us mentioned depends on whether it will be used for AI. Why would you expect that to matter? If you do care about it, it's a pretty good bet that any new data center being built today is for AI.
Not really. Heavy duty training involves intensive energy use. And one of the genuine problems with AI data centers is the electricity use can be very high or very low with minimal warning to the grid operators. This is part of why it pushes up electric costs. I'm not sure what evidence you have that any new data center now is being built for AI. Many of the data centers being objected to are small "Edge Data Centers" used primarily to reduce latency for video streaming, video games, and other activities which require low latency https://www.maysteel.com/why-maysteel/resources/blog/types-of-data-centers-how-do-you-choose-the-right-data-center.
Putting solar panels on the roof of a data center is not much more than a fig leaf. Solar panels can produce around 200 W per square meter, but only in the daytime. A rack in a data center that takes up around 1 square meter can consume a few hundred times that much.
So, first putting solar panels on is a step. It doesn't do everything, but it is a good step. It also has the nice advantage that if there's a serious bust in data centers, there will be already solar panels ready to be connected the other way for the grid. But you are also underestimating the effectiveness of solar panels, for a few reasons. First, almost no data center is used at 100% capacity. The solar panels keep producing even when server racks are getting little use. Second, data centers require corridors for humans to move, office spaces for humans who work there to stay, along with bathrooms and other needed things. Typically, actual server space takes up around 20-25% of the actual space. Now, that's not quite as good as it seems, since data centers are often 2 or 3 floors. But overall, the ratio is still better than you state.
But if you think that's not enough, then you can make it tighter. You can do things like require that their parking lots have solar panels too. Or you can even just require a specific percentage of their power be handled by solar, and then let them figure out the details, including attached solar arrays if needed. But these are all conversations we can have, and far more useful than just saying "No!" very loudly.