From what I've read from hours of browsing this forum is that you do indeed have to specify your interests to a very specific program in your statement of purpose. I'm applying to neutrino experiment programs this upcoming season. I think that is specific enough, like I don't think I'll have to specify whether or not, and why, I'm interested in astrophysical neutrino exp or high energy neutrino exp. But I think simply stating "interested in particle physics" is far too broad.
From what I've read, it looks like whether or not you specify theory or experiment affects the outcome of your application. Theory is supposedly much harder to get into. I don't think it's recommended to lie about what program you're interested in, and switch once you're admitted. I'm not too sure what the variance, in terms of admittance, is between different experimental or different theoretical programs are but there is evidently a clear divide between theory and exp.
Regardless, you should apply for whatever subfield you're genuinely interested in. If you're passionate and qualified, things should work out. At least that's what I'm hoping haha.