Contrary to popular belief, there are actually three options. You can disagree with something by not upvoting it (instead of downvoting it). On beehaw, you can get an indicator of what the overall community thinks of a response by seeing whether or not it has a significant number of upvotes relative to the rest of the content around it.
I find that anything that I would want to downvote should instead be reported anyway. I reserve downvotes on other platforms for posts/comments that are made in bad faith, which on Beehaw is often enough to report for anyway. On other platforms, I’ve seen downvotes used in exactly the way you describe, and it’s led to at least me wanting to interact as minimally as possible knowing that as soon as I post something, some bot might just downvote it right away, immediately influencing the kinds of responses I get because apparently many people operate as part of a hivemind.