My email and LinkedIn has been blowing up with recruiter messages. I want to come up with a system to funnel them down to a manageable number of leads. Would it be rude if my first email to them is asking the TC range and whether they are willing to sponsor visa and green card? I will do it politely and explain why I'm doing it (to save time) of course.
Not rude at all, if you are clear and polite. Anyone will love if their time could be saved.