This forum does not provide secure anonymity; however unless someone was imprudent about disclosing enough info about their identity, I can't see that any info shopper could pin down someone's identity with sufficient confidence. OTOH I think that if someone actually knew me and was also a regular reader of BF they could probably figure out my user name.
Nevertheless, it is an important point to avoid posting anything confidential or embarrassing on any online forum. If you don't want to tell your spouse, sibling, friend, boss, or coworker; you should not be telling me on this forum.