What does "sectarian" mean on this train poster?

Just to add to Nigel J's answer and particularly that it is a regionalism.

The Scottish Government have an Advisory Group on Tackling Sectarianism in Scotland. This, in itself, shows that they feel sectarianism is something to be tackled.

In 2015 they came up with the following "working definition" of sectarianism:

Sectarianism in Scotland is a complex of perceptions, attitudes, beliefs, actions and structures, at personal and communal levels, which originate in religious difference and can involve a negative mixing of religion with politics, sporting allegiance and national identifications. It arises from a distorted expression of identity and belonging. It is expressed in destructive patterns of relating which segregate, exclude, discriminate against or are violent towards a specified religious other, with significant personal and social consequences.

see section 3.9 of the interim report

By 2015 they proposed a new one:

Sectarianism in Scotland is a mixture of perceptions, attitudes, actions, and structures that involves overlooking, excluding, discriminating against or being abusive or violent towards others on the basis of their perceived Christian denominational background. This perception is always mixed with other factors such as, but not confined to, politics, football allegiance and national identity.

see Section 5 of the 2015 report

Without delving into what these mean, it does show that the word "sectarianism" is used in Scotland, especially, in a particular sense, and that even the Scottish government doesn't quite know what. It refers to a culture dependent on people seeing themselves as members of either the Protestant community or the (Roman) Catholic community, and to generations of rivalry, at least, between them.

In Glasgow particularly Rangers is supported by Protestants, and Celtic by Roman Catholics. There are wider loyalties beyond Scotland to other parts of the British Isles, with Rangers fans often waving Union Jacks and Celtic preferring Republic of Ireland flags.

Supporters of Rangers and Celtic have many traditional songs, some of which contain phrases which most people would consider offensive such as "F**k the Pope", or Queen, as the case may be. Others do not contain anything particularly offensive in themselves, but if sung on a train, by a group of young men or teenage boys, for example, may result in a response from another group, and while this may be good-natured, it often isn't, and can end violently. Even if it doesn't, it can be un-nerving to other passengers.

The Scottish Government claim that this law is intended to reduce such happenings, but opposition parties are generally opposed to it and it is under review. While poor relations between Protestants and Catholics, and football violence, or violence at other community events (e.g. Orange Parades involving Protestants), is a problem; the Scottish Government is pro-independence and has been accused of being uncomfortable with loyalties beyond Scotland.

It does not prevent two friends discussing their divergent theological perspectives; and this particular rule does not apply in England, Wales or Ireland. but only in Scotland.

The posters on Scottish trains relate to the Offensive Behaviour Act which is designed to tackle football violence.

As @NigelJ has said, much of the issue surrounding football is linked to religion. In Scotland, this conflict, which is as much cultural and political as it is religious, is archetypally seen in the Central belt where support for the football teams collectively and colloquially known as 'The Old Firm' is traditionally aligned on Roman Catholic support for Celtic and protestant support for Rangers.

The antagonism between these branches of christianity is not confined to football and also accretes round events like Orange Walks and is underscored to some extent by segregated education.

This divide between the communities represented by the different branches of Christianity is widely described as 'Sectarian', to the extent that this is the default understanding of the word in Scotland. Sectarianism in Glasgow, the central belt and Scotland generally is a wide subject which I will not attempt to tackle in detail, but the wikipedia link and associated Talk page gives a decent grounding.

'Sectarian language' as referred to in the poster, is therefore to be understood as language deliberately intended to antagonise and provoke members of the 'opposing' community and will be understood in that light by those to whom it is relevant.