7 Remember those who rule over you, who have spoken the word of God to you, whose faith follow, considering the outcome of their conduct.
8 Jesus Christ is the same yesterday, today, and forever.
9 Do not be carried about with various and strange doctrines. For it is good that the heart be established by grace, not with foods which have not profited those who have been occupied with them.
rule (v.7) = guide, leadership
follow (v.7) = imitate
outcome of their conduct (v.7) — the way they lived, probably including those in chapter 11 and more recent leaders
Verse 8 shows Christ as the object of the faith in verse 7.
Clearly Hebrews 13:8 and similar verses such as Malachi 3:6 (For I am the LORD, I change not) are not intended to be applied to physical truths, but rather to the unchangeable nature of the Godhead. Always holy, always perfect, God demonstrates His attributes in verses such as Isaiah 11:2. God is love, and so much more: and it is those attributes which are the same yesterday, today and forever. — M.A.D. about Hebrews, by Terence, D. McLean, page 192.
do not be carried (v.9) — tense indicates present danger — (here) rejecting Christ as Messiah and returning to Judaism
grace (v.9) — the inward purification of the new covenant
foods (v.9) — the ceremonial observances of Judaism
Previously, meats were said to belong to them that are of full age, and strong meat was spoken of favorably (Hebrews 5:13-14), unlike the verse above. McLean, page 192.