Fundamental differences - case by case

So how do I this resolve fundamental differences in perspective between players and DM about the roles each has in decision making?

Most often - case by case. Really. Please don't expect a universal answer working for all sizes for such a deep question. Or please make it a separate question, offering more details about how those perspectives differ and what you've tried to resolve them. Same page tool comes to mind as one potential help. I've tried in your final question to offer a helping hand to some extent.

Are you in the right - I'd say yes but that depends

Am I in the right for making the decision I did?

I'd say yes, for two reasons.

1. For me, a group takes precedence over a campaign.
2. You've extended an invitation to the guy. He accepted it. You never rescinded the invitation. I read nothing that mentioned others (this large minority) ever inquired about it or asked you to or had an assumption the guy didn't get the invitation. So, he was just late.

Still, with that, it depends. The real question here is... What's the social contract in your group? Contract of a group, or that of a campaign? Which comes first?

In my groups (4 different ones), if we started a side-campaign cause someone would be missing, we would welcome that missing person anytime. Cause they're a part of the group already. Everybody would chip in the narrative to make the old-new character "better-tied" to side-campaign's plot.

That doesn't seem to be the case for you though. Why? You can probably answer better than we can - it's your group. Is somebody in this minority afraid they'll lose their narrative once the latecomer joins? Were there conflicts (playing styles, in-game, between players, ANY) Perhaps somebody is having a time of their life now and latecomer would spoil it, steal the limelight? Try answering these questions and you may hit upon a solution.

How to resolve/repair

1. Convey your motivation/reasoning, without pushing it.
2. Learn theirs.
3. Reach out a compromise.

The difference between resolution and repair here is how much this compromise leans towards you or them. They don't want to accept the latecomer, the question is WHY EXACTLY. If their problem is botched narrative, ask them which points speficically they want assurances on and give them the assurances. If they are afraid of stolen limelight, hint at some truly awesome scene for their character alone. Etc.

Conveying your motives

1. Tell the large minority about being a part of a group. Tell you felt it's obvious. "I totally did not think a side-campaign meant he cannot come in, he's part of our group".
2. Say you extended the invitation already. Say it was never rescinded. Say it's natural to expect that invitation still stands. Yes, it's not good to come late, but holiday/trip/other good reason makes it acceptable.
3. Explain you never expected this being "just your decision". Say you assumed it was same for everybody. Even if this turned out to be wrong, this is something people very often do. It's a common, human mistake. Admit you're open to that being one such case and ask if it is.

Learn theirs

1. Learn why they believe a long-time player should be denied access now? Despite the invitation to play?
2. Ask how they'd tell him why he can't play now and when will he be able to come back and play again? Notice if the answers change between 1st question and now.
3. Ask them are they all right with being penalized the same way, should they ever miss the beginning of a session (or few sessions in a row)? Even if they do it for good reason (nice and long family vacation, funerals, exams, round-the-world tour or whatever).

Work out rules for next time

Ask the large minority for help with working out a compromise that would be satisfactory. Ask most vocal or deciding person in that group to come with you to tell what you've decided to the absentee.