I can think of at least four ways that that Hebrews 12:14 verse about “without holiness” can be understood.
1) Yes, only Jesus (God) is holy, (and the holy angels), so without His holiness, no one will see the Lord. No one will ~come before the Lord~ in Heaven without Christ’s righteousness.
2) We are made holy ~in Christ~, in the heavenlies, and we are ~declared~ holy. Without this gifted holiness, no one would ~see the Lord~ or even go to Heaven, meaning no one will be able to see God in Heaven, the “beatific vision.“
(Hebrews 12:1 says that sin easily ensnares the believer, so we know that that often could be a problem in the life of us believers.)
3) We have a level of imperfect holiness: the perfect holy Christ coming through us, but imperfectly, mixed in with the sin still in our lives—12:10 talks about being partakers of His holiness. ~This is the holiness that believers and unbelievers could see~.
A fourth meaning could be that without seeking God and ~growing in our gifted indwelling holiness in Christ~, we ourselves will not have the spiritual eyesight to “see” the Lord or perceive His presence as we live on this Earth.
Some people are “holy” in the sense of external righteousness, which is often just arrogant pride.
Others are holy, Christlike, and that holiness and that Spirit, and that love, and that grace, comes from God, not themselves, and people can tell the difference.
But the verse says, basically, “pursue holiness so people can see the Lord coming through you.”
I think we have to be careful that we don’t get caught up in only one interpretation of a verse, based on one overriding belief, if the meaning is not clear. Maybe some verses are a little ambiguous for exactly this reason.