Nothing is 100% safe. It is just a matter of being safer than the effort the attacker is willing to spend gaining hold of the data (or that it will take so long that the data is no longer worth having).
That's not an issue of the security of fax as a transmission method, it's a problem with your company's security at the fax endpoint.
There's also the issue that many fax endpoints that are fax to email gateways. Or fax to non https website gateways.
Edit: Nobody is arguing for using email instead of fax. The argument is to use something better. Like paypal or stripe instead of full cc info + cvv2 on a piece of paper.
When it comes to liability for breaches of confidentiality, yes, it matters very much whether the sender chose an poor channel or the recipient had choose poor practices around what was done with information once it was received.
I see all sorts of things I shouldn't see when searching the pile of papers on the fax machine at a large company for my fax.