As you can probably tell from my user name, this is in fact something I know quite a lot about.
DNA tests from Ancestry are not a con. There are two aspects/sides to testing. The first, cousin matching, is what we genealogists are interested in. The testing company will look at your DNA (which is a long string of letters) and look for sections/segments of that long string of letters which match with other people's long string of letters. The more DNA which matches, the closer the relationship. The genetic closeness is measured in centimorgans, and you can use your DNA results ALONGSIDE CONVENTIONAL GENEALOGY to work out what your relationship might be. Sites may suggest possibilities for a match such as "second cousin, half first cousin, first cousin once removed" or whatever but you need to understand what that all means. The sites cannot say with all certainty how two people are related unless it's a very close relationship like parent-child. But lots of people don't understand that.
The ethnicity estimate is the other side of these Ancestry and similar DNA tests and is far more subjective. Genealogists take these estimates with a huge pinch of salt. They were really developed for the North American/Australia/New Zealand market where most people who are exploring their genealogy know that their ancestors originally came from somewhere else. Doing a DNA test helps them target their research - should they be researching records in Ireland, Italy or Greece? The ethnicity results can be fairly accurate, might not be. My own DNA says 12% Irish which would mean one Irish great grandparent (ish) whereas in fact my g grandparents were all born in Scotland, to parents who came to Scotland during the decades before that, but grew up in Scotland and married within their local community - who all had Irish roots too.
A great grandfather is quite distant - you seem to think OP you have been deliberately deceived and almost cheated of potential Jewishness but it's really not like that. Your grandfather may have been told his own father was Jewish and why would he disbelieve that? The family may have been living in a predominantly Jewish area and people have assumed. Or there is an illegitimacy somewhere along the lines.
This is why traditional genealogy and DNA genealogy cannot operate separately. One complements the other. And yes, treat anyone else's tree on Ancestry with the utmost scepticism. Especially those trees which have no sources/documents attached. There are loads out there which are total mince.