How can I anonymously get Monero with Bitcoin or Ethereum?

[dkbit98]

I'm wondering what the best ways to get Monero without linking it to my Coinbase account are. With the lowest fees possible, of course.

There are several non-kyc exchanges that have listed monero, and Bisq is one of the best options as decentralized exchange.
Other alternatives are LocalMonero or Agoradesk p2p trading, Unstoppable swap, eXch exchange, etc.
Some centralized exchanges still have monero listed but I would be very careful with them.

[RickDeckard]

Is this a phishing site or what? because when I access this site, it says the connection isn't secure.

While xchange.me didn't have such warning.

The website looks like a highly attempt to copy another service which has more reliable background (check my previous post[1] for more information). I actually went ahead and personally warned the user in order to avoid using the exchange but it does seem that there was an attempt to publicize the service even so.
[1]https://bitcointalk.org/index.php?topic=5492144.msg63921944#msg63921944

[Nrcewker]

Pick exchanges or Peer to Peer marketplaces, without KYC, and buy Monero, Ethereum or Bitcoin.
https://kycnot.me/

If KYC is the main issue then P2P is the only solution OP. P2P deals often come with risk, hence I am warning you to be extra careful while dealing with P2P or private deals. You can try bisq, as it has good customer reviews and many trusted traders are present there, else I have personally used Paxful, they allow upto certain limits to trade, but I guess Monero not available there. So yes try the sites available here, and check all the terms and conditions before starting a trade there.