verb + がまま is a fixed phrase from classical Japanese. This が is an old possessive particle (see this question). A phrase like this often has a deeper nuance than what's written literally. Here, がまま has a sense of "without any chance of questioning" or "at someone's mercy". 言われるがまま就活を終了した strongly suggests this person had no control over what he did or did not understand what he was doing.
言われたまま is a phrase that follows the standard Japanese grammar and just means "as [I] was told". If you voluntarily followed someone's instruction understanding most of it, 言われたまま is better.
For example, saying 言われたまま発注しました or 言われたとおり発注しました to your boss is usually okay ("I placed an order just as I was told"). But saying 言われるがまま発注しました to your boss sounds like you're either irresponsible or angry.
See also: What does ～がままになる mean?