there are Palestinian Israelis but although they are nominally citizens they don't have the same rights
There are over 2 million Arab Israelis and they do have the same legal rights in the eyes of Israeli law. From wiki:
" the Israeli Supreme Court has consistently interpreted "Basic Law: Human Dignity and Liberty"[301] and "Basic Law: Freedom of Occupation (1994)"[302] as guaranteeing equal rights for all Israeli citizens.[303"
They don't however have to do compulsory military service as there is an acknowledgement of conflict of interest (eg possibly having Palestinian relatives in the West Bank).
They do tend to attend separate schools as they have different home languages, but they're certainly not segregated from public hospitals etc as you earlier implied.
In fact Israeli hospitals do (did) also treat Palestinians despite them not being Israeli citizens - some of those murdered in Kibbutz Be'eri were active in collecting Gazans from the border to take them for medical treatment in Israel.