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Is there a way to make my e-mail non-visible in my Stack Exchange profile?
Your email is only shown to you and diamond moderators, not to everyone. Recent change requires diamond moderators to click on a link to show the email, it is not visible until then.
Here's how I see your profile (as a 10k user, even):
Only you (and the people who run SO - including moderators) can see your email address. No need to worry about the spammers getting it. :)