[Goater]

These "messianic jews" are believed to be jews who had converted to christianity or jews who took on many christian rituals (which later became beliefs) due to persecution or compulsion.

Generally, Judaism considers someone born jewish to always be jewish - some strains of judaism believe that anyone taking on another religion is no longer jewish, however this is a minority position.

Whatever the history, belief in Jesus as the messiah is not compatible with Judaism and so these people should not be described (in terms of what religious, rather than ethnic group they belong to) as Jews.

Edit: there are many groups of traditional jews that do believe in a messiah - just not jesus - and are more accurately described as "messianic jews". The hassidim are a good example.