The noun schism, and its derivative schismatic, have two pronunciations based on the reading of the letters '-ch-', which represent the Greek letter 'chi'. The traditional academic pronunciation reduced the first sound of schism to a simple '-s-' sound. The religious poet Milton even spelled it 'scism'. Some who like to affect the ability to pronounce Greek aim to produce the sound of the Scots 'loch' or German 'ich'; for most, this results in a pronunciation beginning 'sk-'. (The second '-s-' is always pronounced as '-z-'.) LPD says: "The traditional 'siz-' is being displaced, except perhaps among clergy, by 'skiz-'", and reports that 71% of a British sample in 1988 used the '-k-' pronunciation. OED says "The pronunc. [skizm], though widely regarded as incorrect, is now freq. used for this word and its derivatives both in the U.K. and in North America."
The basic meaning of schism - the word comes, through Church Latin, from the Greek σχίσμα (schisma, a cleft), a noun from the verb σχίζειν (schizein, to split) - is 'a break (between groups)'. Its basic use in English was to mean a split between different groups of Christians over some point of faith (see further Great Schism). This has now expanded figuratively to include sub-groups of any sort of belief or ideology, for example groups that try to break away from a political party to form a sub-group.
The word schismatic may be either an adjective or a noun. As an adjective, it means 'relating to, or promoting, a schism', and as a noun, 'a person who promotes a schism or belongs to a schismatic group'.