I like re-playing RPG adventures and I don't let my knowledge of the module interfere with the way my character follows clues. Should you re-play an adventure, though, there are some important things to keep in mind.
My primary rule is pretty simple. If I can't trace a decision my character is going to make back to something the Game Master revealed during the game, then my character doesn't do it. It might like a lot of mental gymnastics, but it comes naturally as long as you pay attention to what your character knows.
If you feel the largely unreasonable urge to skip ahead of the plot, then stop and ask yourself how your character would have gotten to that point in the plot flowchart. Suppose you're playing an adventure in which it's been established that there's an evil goblin somewhere in the manor. As a repeat player, you already know the goblin is hiding in the attic. Well, you can only go to the attic once you can produce the piece of evidence that would make your character believe the goblin is in the attic. Simple as that.
And you should also refrain from suggesting that the party search every room, knowing that that tactic will eventually necessarily lead the party to the goblin's hiding place. There's a good argument that searching the manor room by room is actually the logical way of locating an intruder, but you're a repeat player. Play the game for the table. Let somebody else come up with a strategy.
It's a roleplaying game. We all deal with metagame knowledge on some level, and re-playing an adventure isn't any different. Play your character, setting aside your knowledge of how the plot unfolds.
Here's a basic example. You know, from having run the adventure a few months ago, that over night a bunch of goblins are going to raid the town. Your character is a lowly farmhand with no military or adventuring experience. Does your character suddenly decide to stay awake, armed with a crossbow, staring out at the empty plains all night until a goblin shows up? Or does your character go to bed as usual because the big harvest is tomorrow and getting rest is important?
That's a pretty obvious one, I think (the correct choice was the latter option). Seldom is an RPG adventure so simple.
Here's a slightly more complex example.
You know the MacGuffin is in a hidden compartment under the owlbear rug. But your character hasn't even gotten the quest to find the MacGuffin yet, let alone know that it exists. Why would your character storm into the room and search for secret compartments? Well, come to think of it, your character is a level 5 rogue. It's arguably second nature to go into a room and give it a quick once-over. Now what?
Restricting your character from doing something that is arguably natural, or even from doing something impulsively, seems like a major limiting factor on roleplay. Actually, though, your character can do what comes naturally or be impulsive, just not about obvious plot points. So the rules are:
It's a balance between playing for your character's class and playing for the rest of your party. It's an RPG. There's always an opportunity for you to discover something unexpected and unique. And if the game's on rails, then at the very least there's always combat.
To many people, the concept of re-playing an RPG adventure sounds like cheating. Worse still, some of the people who re-play an adventure only does it so that they can cheat. I've been a Game Master for enough random people online or at conferences to know that some people read adventures in advance so they can get cool stuff and solve puzzles. (It's especially awkward when such a person loses track of what I've told them as I run the game and what they learned from reading the adventure in advance. "How do you know there's a trinket on the mantle? I never said that.")
If you know an adventure already but you want to re-play it, make sure you tell everybody at the table that you've run it or read it or played it before. Explain to them that just because you know the adventure, it doesn't mean your character does, and that you play true to your character. It might help to use video games as an example (although, to be fair, there are apparently some people who don't re-play video games, either).
If somebody can't wrap their head around that concept, or if they just don't feel like they'll get the same experience by playing with somebody who "already knows what's going to happen" (I'll admit, this is usually somebody who hasn't played much), then consider withdrawing from the game. But if everybody's comfortable with it, then proceed. Play the adventure. Again.
Re-playing an RPG adventure is a great way to see a story from a new perspective. It also reveals a lot about tabletop RPG. When I re-play an adventure, I'm sometimes shocked that it's the same game. Every party is unique, the Game Master might change plot points and other elements, and besides that your character is different. There are almost more opportunities for an adventure to not be the same as before than there are for it to be the same. Give it a try. It might surprise you.