By default, the MX doesn't have any rules blocking against outgoing. Assuming the SMTP you are trying to relay through is external there is no reason that should be blocked.
But a good practice, if O365 supports it, is to setup your relay through O365. In our G Suite environment, I have it setup as an SMTP relay with and it just whitelists my networks WAN IP. That way I can relay through our own e-mail environment rather than relying on a carriers SMTP. This also becomes important if you ever start looking into SPF, DKIM or DMARC.
Adam R MS | CISSP, CISM, VCP, MCITP, CCNP, ITILv3, CMNO
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