No they won't. But some exchanges, like Coinbase, will mark your account if your coins are tainted, and will sometimes freeze your account, and confiscate your coins.
One more reason to not use Coinbase then. Any exchange that goes beyond the necessities of KYC / AML should be avoided like the plague. If you get your account frozen on the likes of Coinbase you should have stuck with PayPal. Same difference, but without the extra steps of going through crypto.
It goes back to the debate. What kind of users have too much to hide that are incentivized to pay for tumbling, and why should I mix my coins with their coins?
Would you, personally, post your bank statements publicly on the internet?
What is the estimated, average fee to mix 1 Bitcoin?
Wasabi Wallet charges 0.003% per anonymity set which apparently comes down to 0.15% per transaction [1]. ChipMixer relies on donations and can thus be used to mix for free, but will keep any amount smaller than 0.001 BTC as donation [2]. Other options likely fall within similar fee ranges.
[1]
https://www.reddit.com/r/Bitcoin/comments/9sziy5/privacy_wasabi_wallet_10_is_finally_released/e90mlvu/[2]
https://chipmixer.com/faqOr people with something to hide.
Not being able to keep private from governments is a threat to democracy. Heck, to any free society that relies on a centralized, hierarchical government.
As is the thinking that only "people with something to hide" want privacy.
Remember East Germany. I don't even want to imagine what a modern day Stasi could do with modern technology and data at hand.