They are. Broadcasting transactions generally won't leak privacy more than your SPV wallets. Even if they were to collect data, they would only get as much data as your browser leaks, which in the case of privacy conscious ones, it isn't that much. I would recommend using a privacy-centric browser and using a new identity for each session, which in normal circumstances can't provide sufficient data regardless.
If you were to use an online tool to broadcast bitcoin transactions and want to maximize privacy it is best to use their API instead of their webpage because through the API and using a simple app all the privacy leaking methods (cookies, browser exploits, JavaScript exploits, WebRTC exploits, browser fingerprinting,...) will be eliminated all at once simply because that way you know what you are sending them whereas it is very hard to know everything your browser sends them even if you are using a privacy oriented one with privacy related extensions.