That's why projects that claim to "pollute" your browsing history like RuinMyHistory, noiszy, adnauseam, and TrackMeNot are not only pointless but also dangerous.
The data being collected about you will always be used against you, no matter if it is accurate or not. If your browser randomly browses to webpages that gets "this person is a muslim" or "this person is gay" added to your dossier it doesn't matter if it's true or not, when your next would-be employer or would-be landlord who hates muslims or gay people uses a data broker for "background checking" and sees that, you're not getting the job/apartment. They won't tell you why, you'll just be rejected/ghosted.
If you're a 40 year old man, but your browser add-on convinces a data broker that you're a 34 year old woman seeking an abortion, that data can still cause you end up the target of a lawsuit in Texas and it will take a non-zero amount of time and money to clear that up.
If someone in your zip code kills someone using a certain type of plant, or household cleaner/chemical, or medication and your add-on has been browsing sites about that thing, you can end up on the police's suspect list.
If you only make $30,000 a year but your add-on searches for yachts and expensive jewelry often enough to convince a data broker that you've got tons of money then it doesn't matter that the data is wrong, the next time you try to book a hotel or order something online you can still be charged a lot more than you would have been charged otherwise.
Handing extra fake data to people whose only goal is to use data against you is just handing them more ammunition. It doesn't matter if it's "garbage" to you, it's still something they can and will eventually use against you. You cannot know what will prejudice someone against you. The more data is in your dossier, the more opportunity there is that you'll meet the right (or wrong) criteria.
No data broker is going to look over your dossier and see that there's inconsistencies and go "Damn it! This genius has ruined my data! Now I have to throw all this data away as it is now worthless!" They aren't even going to look over your dossier. They're going to get paid to hand over a list of people flagged as being 'X' and your name/address/identity will show up along with everyone else flagged as being 'X' even if your name gets pulled up again when someone else pays that same data broker for 'Y' which is the opposite of 'X'. The data broker gets paid either way.