No single check decides. A site scores the visit: what network the address belongs to, whether the browser's details fit together, how fast pages are requested, whether the mouse moves. A high score brings a captcha or a block.
A proxy only answers the first question, the address. If the browser itself gives the program away, a clean address will not help. This is why people pair proxies with a real browser, sensible speeds and, for separate accounts, an antidetect browser.
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