I build in public and think about these two things often.
As an indie dev, I make around $800k per year on my two saas companies.
Copycats: There have been some, but the saas companies that I've build have such a hard cold start problem (they're social marketplaces), that all the ones I've seen pop-up flatline. If you have a product that has no moat, sure, don't build in public.
Bragging: In fact, it's the opposite. When I post something, and the comments start rolling in, it's only then that I realize mistakes I've made or things I could've done better.
---
I think building in public is still a decent way to build an audience and to get free insights.