The phrase "free speech" does not typically mean "free as in beer," rather it means "free as in freedom," so in this case you're conflating the two meanings of "free" in English.
The fact that Twitter is login-gated makes it objectively less free as in freedom.
Generally we in the western world consider ourselves 'free' citizens. Yet to live this life you need to register your birth, get a social security number, and enroll in education etc.
I dont see signing up to twitter any differently to this. You register with an email address and you are granted access. Similarly to registering a birth and being granted access to 'society'.
Indeed, fair point. I've conflated those in my comment above!