Reform Judaism does not view the Sabbath as irrevocable holy day and the movement which started mid 19th century grew considerable so that your remark "they were indistinguishable from non-jews European people and led similar lives outside of religious matters" is only valid for this branch. I would even say that the integration and non-conspiciousness of Jews in the modern world (they still follow many rituals and traditions, so you can recognize a Reform Jew if you are a good observer) is only possible with the creation of Reform Judaism. Saturday is therefore not a problem for integration.
As reaction the ultra-orthodox Jews (Haredim) were moving in the opposite direction which means separation from other denominations, denial of the modern world and strict observance of Jewish law. The Haredim did not integrate into the western world at all and their distinctive appearance means they are very easy to recognize. The relationship between Haredi and Reform Judaism are for this reason a bit...strained.
The rest of the Jews who were more conservative, but would not decline to participate in the modern world are the Modern Orthodox branch. They try to balance the observance to traditional laws and the requirements of modern life. According to the 1990 National Jewish Population Survey only a minoritymajority of 15%78% Orthodox jews consider themselves Sabbath observant.