Possible? Yes.
Easy? No.
One way would be to write a small custom Bitbucket plugin that would emit a little bit of JavaScript or CSS on the Pull-Requests page to disable the like button on page-load.
It would be a bit brittle though and you'd need to keep an eye on future Bitbucket versions in case the HTML of the Like button ever changes (and thus breaks your JavaScript or CSS logic).
If you have a valid Bitbucket Server license then Atlassian makes the source code of Bitbucket available through my.atlassian.com. Very handy for questions like this!
grep -r likes-button bitbucket-6.0.0-source/
bitbucket-6.0.0-source/bitbucket-parent/plugins/comment-likes/src/main/resources/static/bitbucket-plugin-comment-likes/internal/feature/comments/likes/controller.js: .find('.comment-likes-button');
[etc...]
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Here's the "context" you'll need to reference in your <web-resource> element in your atlassian-plugin.xml to have code appear on the pull-requests screen:
<context>bitbucket.page.pullRequest.view</context>
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