"Please switch to a public Steam profile before attempting to sync" even though it is

It's an issue on Steam's end, not SG's. Given that it usually accompanies other visible issues, it can be determined to be due to instability within Steam servers (which happens all-too-regularly, making this a commonly discussed issue). There's nothing to do but wait and try again later.

That said, in most instances, the problem seems to clear up within about 10 minutes or so, unless the servers are completing borking out. So perhaps just try again in another 5 minutes or so- it's not as though there's a Steam Sale up, or the weekly scheduled maintainence, and the Steam servers themselves aren't completely down, so it's likely enough to clear up fairly quick.

Strange it is happening to me now as well, it won't allow me to enter any giveaways at all on SG until it syncs but every attempt fails. Last time this happened it lasted a couple days and spontaneously fixed itself.

Steam returns a generic error when it can't complete an API request. SteamGifts assumes this error means that your profile isn't public, and that's probably the most common thing users encounter, but it can also mean Steam servers aren't working or SteamGifts hit its API limit.

If your profile is already public, just try again later since it's an API problem and not a you problem.

Happening to me too

Sign out and sign in again should fix the problem

I never encouraged this error on my own. But I do see tickets about it.

Sadly nothing we can do about it. If SteamAPI does not work properly - we can't sync account.

It's just happening to me right now. Signing out and in didn't solve.

SG says "Account is out of date. Synced with Steam 1 week ago.", so it looks like it's giving trouble syncing for a while.