Static or dynamic addressing is irrelevant to MTU settings. For IPoE connections the minimum MTU should be 1500. For a PPPoE connection the maximum MTU is 1492 unless your ISP supports baby jumbo frames per RFC4638.
With a mix of connections supporting differing MTU sizes you either end up with packet fragmentation or larger packets being dropped if fragmentation is not permitted.
Path MTU discovery https://en.wikipedia.org/wiki/Path_MTU_Discovery should resolve this, but misconfigured/broken implementations can prevent this operating correctly.
MSS clamping is often employed as a workaround - this reduces the suggested segment size during a TCP handshake to ensure the packets will not be fragmented.