Your original point is that the right to life is specifically guaranteed by the first amendment. The quote from Justice Jackson was part of a broader point about how fundamental rights should be beyond politics and does not support your argument. Here is the opinion: West Virginia State Board of Education v. Barnette.
The Gobitis opinion reasoned that this is a field 'where courts possess no marked and certainly no controlling competence,' that it is committed to the legislatures as well as the courts to guard cherished liberties and that it is constitutionally appropriate to 'fight out the wise use of legislative authority in the forum of public opinion and before legislative assemblies rather than to transfer such a contest to the judicial arena,' since all the 'effective means of inducing political changes are left free.' Id., 310 U.S. at page 597, 598, 600, 60 S.Ct. at pages 1014, 1016, 127 A.L.R. 1493.
The very purpose of a Bill of Rights was to withdraw certain subjects from the vicissitudes of political controversy, to place them beyond the reach of majorities and officials and to establish them as legal principles to be applied by the courts. One's right to life, liberty, and property, to free speech, a free press, freedom of worship and assembly, and other fundamental rights may not be submitted to vote; they depend on the outcome of no elections. [319 U.S. 624, 639] In weighing arguments of the parties it is important to distinguish between the due process clause of the Fourteenth Amendment as an instrument for transmitting the principles of the First Amendment and those cases in which it is applied for its own sake. The test of legislation which collides with the Fourteenth Amendment, because it also collides with the principles of the First, is much more definite than the test when only the Fourteenth is involved. Much of the vagueness of the due process clause disappears when the specific prohibitions of the First become its standard. The right of a State to regulate, for example, a public utility may well include, so far as the due process test is concerned, power to impose all of the restrictions which a legislature may have a 'rational basis' for adopting. But freedoms of speech and of press, of assembly, and of worship may not be infringed on such slender grounds. They are susceptible of restriction only to prevent grave and immediate danger to interests which the state may lawfully protect. It is important to note that while it is the Fourteenth Amendment which bears directly upon the State it is the more specific limiting principles of the First Amendment that finally govern this case.
West Virginia State Board of Education v. Barnette wasn't a fifth amendment case, and as such did not mention it except in the broader point as quoted above. The right to life is specifically protected by the fifth amendment, not the first.
No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger; nor shall any person be subject for the same offense to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation.