Genealogy /
Ruchla (or Rochla) Andrelewitz / Morgowicz Morgovich [8]
I'm actually surprised with using the word żyd.
I have only come across starozakonny and wyznanie mojzeszowe (the previous in the books I have personally gone through and the latter online but I guess it all depended on the parish and the years). What kind of document was it? Perhaps it's because it wasn't a church book.
As for geneteka -not all parishes are indexed. IME some of my ancestors are indexed, others are not -like great grandparents and their ancestors on my paternal site - even though the books from the parish are available at szukajwarchiwach.pl. or another great grandfather - I know the year he was born, his parents names and even though his siblings' births are indexed, his isn't. He's not in the parish books so they must have been living in another, not yet indexed parish. There are parts of my family I have been able to track online up to 1770s and others where I got stuck in the 1890s.
As for metryki at genealodzy -there are even fewer parishes as at geneteka people index also books from other sources. Finally, there are very few Jewish books there I believe so need other sources as Jewish births, marriages and deaths were recorded in Catholic books only till 1820s or so.
So please keep in mind that some people you find at geneteka might not be your ancestors but someone with a similar name - you need to know the parents names to confirm it's the person you're looking for. Some records give lots of information (like the mother's father's name) but you need to find the correct record.
As for baptisms of Jews I have come across one or two records in allegata books. I don't know if that was the rule but that's a clue of where you might be looking. There's other information there as well, of course.
Finally, the language. Keep in mind, you're not looking only for a Polish speaker but also someone fluent in Russian if it's about 1900s in Eastern Poland. And it's not modern Russian. And it's cursive.
Sometimes it gets slightly easier as there are indexes of people born, married or dead in a given year at the end of the book but the indexes are in the cyrillic usually. In most books written in Russian even though the entries are in the cyrillic, the names of people it concerned are in the Latin alphabet in brackets - although I have come across a church book entirely in Russian.
For other regions you may need someone fluent in German and Latin. If your ancestors converted only in the 1900s, then their birth records should be in Jewish books and I don't know what language they were held in. It might have been Hebrew, Yiddish or Russian (since Catholic priests were told to keep their records in the cyrillic, I guess the same rule applied to rabbis).
Have you tried contacting the state archives in Białystok? What parish are you looking for in Vilnus?
Archiwum Państwowe Białymstoku
ul. Mickiewicza 101, 15-257 Białystok
sekretariat_ap@bialystok.ap.gov.pl