100% and 1000x times this. LibreSSL does have some minor incompatibilities, but those were mostly about removing obscure and very rarely useful APIs that were badly designed in the first place. It was quite likely that if your program used these APIs, it had security issues that OpenSSL couldn't solve with an update.
(Usability is security. If it's hard to use correctly, then it's easy to create a security hole.)
Remember folks, LibreSSL comes from the same people who made OpenSSH, and that "other" OS that had 2 remote holes in almost 30 years. You already trust them, you maybe just don't know it.