To some extent this depends on the field and where in the process you are (although I have to find it funny that 30 applications is considered severe; in math there are positions which get literally 300 or 400 applications). Here are some relevant considerations:
Are you in a field which usually uses Google Scholar? Math for example doesn't almost at all(Edit: See comments by Dmitry here- I may be seriously wrong about how much it is used in math), but it seems to be common in some other fields. If one is one of the fields where it is common, that may make more sense.
Is this is a position where research is going to matter? If you are hiring someone as an adjunct as you suggest, this doesn't seem like a research focused position, so why should it matter?
What stage in one's selection process is one in? If for example one first selects out some of the candidates, and asks the remaining pool to do so, that looks a lot more reasonable. You can probably eliminate a fair number of candidates simply by not having strong CVs (and frankly it is likely if you are looking for a research position in a field that often uses Google Scholar that those people will often be the ones without Google Scholar profiles).
Legal issues are complicated, and we can't really give legal advice here, but there are some potential issues that can be highlighted. The most obvious one is accessibility: is Google Scholar easily accessible for people with disabilities? If it isn't, this would be a potential problem. Are you at a state school or a private school? If a state school there are a lot more rules about hiring generally that need to be followed, and asking for something like this after the job has already been advertised with instructions on what to do will be a problem in some states. Note that in some respects for some of these issues this may also be the sort of thing where it is better to ask for forgiveness than permission: if you ask a university legal counsel if you can do anything that seems remotely questionable, they'll frequently just say "no." If you are in Europe some of the legal issues may also be more severe as they may interact with European data privacy issues, and that's a serious enough issue right now that if one is concerned about it, getting competent legal counsel may make sense, but you may have someone even in IT who can walk you through any relevant issues at an informal level.
Now for my personal opinion: For what it is worth, if I were applying for a position and they asked me to make a Google Scholar profile, since we don't generally use them in math, I'd consider that to be a serious red flag about what the committee knew or how much the school was micromanaging hiring decisions. Unless it was a high profile school, at a highly desirable position, I'd almost certainly say no. And if I were to see it while applying for a position that was a primarily teaching position, my reaction would be extremely negative. I have seen positions that ask one to highlight which of one's research papers one is most proud of, and it might be a substantially more useful than trying to use some potentially gameable metric like this.