Is it safe to buy Bitcoin with cash?

Let's say I bought few bitcoins by cash in currieries exchange. Like, I gave some money in cash, they send for me some bitcoins.

What I am worrying about, where from those bitcoins come. Maybe, someone sell tons of drugs, weapons or something and then transfer those Bitcoin to me. And if I send this Bitcoins to some centralized wallet like Binance that could looks like I sell those drugs.

So in theory police could think I did something illegal, even if I didn't.

Am I right?