... company with sensitive customer relations
Given that many common mail clients support at least S/MIME by default, it actually makes sense to use it. This means that mails should at least be signed by S/MIME. Signing does not cause any problems when mail clients do not support it, but provides solid sender authentication for S/MIME capable clients and thus additional protection for customers against mail spoofing. To make it easy for customers the signing certificate should be issued by a public CA though, which is already trusted by the client.
One might argue that DKIM together with DMARC provide similar protection. But in practice support for these is less common in mail clients, which means that the client must rely on their mail server to properly check both - and most actually don't. Also DKIM+DMARC only cares about the sender domain and not the actual sender. But it makes sense to use DKIM+DMARC in addition to S/MIME signing.
Using PGP instead does not make that much sense. Contrary to S/MIME PGP does not rely on a central PKI and thus there is no easily established trust relationship to the sender. Instead each customer would need to be explicitly trust the senders key, a concept many customers will not properly understand.
For more sensitive B2B communication it makes also sense to not only sign the mails but also encrypt it. There are several mail gateway products which offer centralized automatic S/MIME handling for such use cases so that the whole process is mostly transparent to the employees.