The ACLU still has free speech lawyers, and I supported the ACLU to the tune of 1k last year. But logically it follows that supporting the right of African Americans to survive encounters with police, or for Transgender people to have healthcare, increases the amount of free speech in the world by ensuring their voices can speak in it. A decrease in the survival of people is necessarily a decrease in free speech.
The right of people not engaged in violence to survive police encounters is a natural/inalienable right and a right to healthcare are not similar classes of rights. The former is a "negative right", or liberty, from harm by others (the police), whereas the latter is a "positive right", or entitlement/privilege, to goods & services provided by others.
The Bill of Rights was primarily all about liberties / negative rights, whereas since the 20th century people have started talking about entitlements as rights, when they're not, because that entitlements ultimately must be provided by others (primarily through taxes, but also in constraints/mandates on the behavior of others, e.g., limitations on striking by police or other services, the requirement to register in the draft / Selective Service for men, & eminent domain). Government entitlements typically involve the involuntary actions and compelled behavior of people.