The gatekeeping and phoning home (even though it is privacy conscious). But it's not a strong objection. In general I prefer browsers to be neutral by default and make no HTTP requests behind the scenes, but I acknowledge that's unreasonable for most users. It's less about my personal objection and more about an objection to on-by-default corporate decision making being deployed to millions of users.
While safe browsing hasn't come under much scrutiny due to its limited scope and that it hasn't been abused, I suspect it won't be long before someone's site has its ads blocked unfairly by the coalition. I understand with human review and pending-vs-actual-blockage incubation they are attempting to alleviate false positives, but the internet is too large IMO and the rules are subjective (so I can have a site with a 29% ad density?).
Out of curiosity what is your objection to the Safe Browsing lists?
I personally have my router blocking sites at the IP level and DNS rejecting queries for domains off this list.
I can't remember the last time I couldn't visit a site because it was on the list but with the prevalence of zero-day malware and naive users on my network, I'd rather just not even deal with the potential.