The answer is a "NO", but not a clear no, as there is a maximally pessimistic view that could be contrived to say "YES". I will tell this story here, and only once:

First, Bitcoin is like a train. If you try to stand in front of the train, you will not stop it, you will only hurt yourself.

Bitcoin is not private by default. It is pseudonymous for anyone who generates new transaction addresses. Even if a specific address is proven to have obtained their funds via "naughty" activity, it only costs a single transaction fee to introduce doubt as to who owns the coins.

Bitcoin has many overlapping privacy protocols. If someone is not granted permission to use one strategy, they will fall back to the next, then loop back into the first. Any censorship attempt can only delay the movement of coins, not direct them somewhere else.

Wasabi is a fully verifiable open source project, both the client and the server. Users can't verify what code the server is actually running, so all privacy protections are enforced purely through the user's client.

Wasabi's privacy is so strict that it is almost impossible for users to opt out, because privacy weaknesses of one user will compound to affect every user in a coinjoin. The wallet syncs using BIP157/158 compact filters, preserving the privacy of on chain transactions for light wallet users, while reducing the bandwidth cost 99% vs a full node.

Wasabi uses a unique Tor IP by default for every single parallel connection. The client connects to 12 Bitcoin peers, each through its own Tor IP. Every tx broadcast, coinjoin input/output registration, and update listening handler uses it's own Tor IP.

This means that the server operators for syncing or coinjoining NEVER learn user transaction data, and the privacy policy volunteered zkSNACKs a legal target if they did: https://bitcointalk.org/index.php?topic=5476197.msg64000959#msg64000959

Users are always in sole custody of all of their financial history, as it should be.

Second, Wasabi was formerly a corporate product created by zkSNACKs ltd, and two of the cofounders were lawyers. zkSNACKs had 40+ employees (whose salaries were paid exclusively with Bitcoin) and an office in Europe, and they received intimidating letters in the mail.

As a sign of good faith, zkSNACKs implemented "Chainalysis" (not the actual company used, but we'll use their brand like we use "Google") on the COORDINATOR SERVER ONLY to avert interacting with coins that are involved in high profile accusations. Since the coordinator code is open source, anyone could have copied and pasted the code zkSNACKs created without inheriting their R&D costs: https://bitcointalk.org/index.php?topic=5476197.msg64067143#msg64067143

People who understood the truth decided to use this as an opportunity to dishonestly smear their opponent. The simple fact is this: Wasabi can't collect your data for chainalysis, and never did. What actually happened is that zkSNACKs bought data from chainalysis to build a blacklist. This is a slippery slope towards a loss of freedom, but it is not fraud, not theft, and not worth talking about anymore.

seeing as the status quo advice seems to be "do nothing,"

They are cowards who don't want to take free money.

and follow the heaviest chain.

Spoiler: This will absolutely be Core, not Knots.

Is there something about having the same coins on both chains that exposes you or is this only necessary if you want to sell the fork?

If you don't care about your Knots coins at all and consider them literally worthless, then you can spend your coins on the Core chain without any worry as if the split never happened.

Also, can you explain the heuristic of gaining replay protection by coinjoning? The advice I have been seeing is to split coins via RBF.

That advice is correct, @Murch is a genius and a saint. What coinjoins do for you is help you avoid needing to hassle with that. As soon as ANY replay protected coin enters the coinjoin pool, all future descendants that combine with it will inherit replay protection. So, if you wait a day after the chain split and then remix your entire wallet, you can be sure your addresses won't get drained on the Knots side of the split.