There is some evidence, not a whole lot by most people's standards, but plenty for the kind of wild assumptions and speculation beloved of Irish medievalists.

The evidence for the worship or veneration of Thor comes in three parts: 2 mentions in texts and a few archaeological finds. Firstly, in 995, the King of Tara Mael Sechnaill II attacked Dublin and took away "by force" "the ring of Tomar and the sword of Carlus", according to the Chronicon Scottorum. We don't really know what these are, but they seem to have had some sort of ritual or symbolic importance to the Dubliners, or why bother taking them at all, right? Tomar is almost certainly an Old-Irish rendering of Thor (it would be written Tomhar or similar in Modern Irish, with a lentition on the 'm' producing a soft 'v' sound - pronounced toe-var or toe-war), but we have no idea who Carlus is, and he usually tends to be forgotten about in all the excitement over the only Norse god to have his own film and comic-book franchise.

The second written reference comes only 5 years later, when the Munster-based Annals of Inishfallen record that Brian Boruma, the new king on the block, besieged Dublin on the 1st of January 1000, having defeated the city's army the day before at the battle of Gleann Máma. Brian's army burnt a place called Caill Tomair as firewood, we are told, but nothing more. Again, this place must have had some symbolic value to the Dubliners, or else why mention it? Tomair is the genitive form of Tomar, so the place obviously has something to do with Thor, and Caill is usually taken to mean wood or grove (cf. Modern Irish coill, wood), which makes sense if Brian's army used it for firewood. But these are the only two mentions of Thor, or indeed paganism in Dublin, in the Irish written sources.

The archeological evidence consists of several Thor's hammer amulets unearthed in excavations in Dublin by the National Museum - IIRC some are on display in their Viking exhibit in the Archaeology museum on Kildare Street. Altogether though, it doesn't really add up to much and, despite people's love of imagining pre-Norman Dublin to be a 'Viking' pagan city, I don't think it can realistically be seen as anything like that after c. 920 at the latest.

Firstly, Irish authors never really fling the pagan label around about 'Viking' Dublin. After the first generations of Viking raids, they're almost always called 'foreigners' (gaill), not pagans. This reflects the fact that almost all Dublin Vikings were born in Ireland (or sometimes England or Scotland), were often of mixed parentage: the first known intermarriage between a Scandinavian leader and an Irishwoman happened in 883 and Sitric Silkenbeard, king of Dublin during both incidents in which Thor is mentioned, was the son of an Irishwoman and was married to an Irishwoman. Old Irish was probably more widely spoken than Old Norse in Dublin and bilingualism seems to have been the norm even for those who spoke Norse. The majority of the population was probably Christian throughout the city's history (Christian cemeteries at St-Michael-le-Pole, near modern-day Aungier Street, Castleknock, Kilmainham and Islandbridge all continue to be used uninterrupted) and furnished burials outside of cemeteries (i.e. burials with weapons and other grave goods) are the only real indication of any 'pagan' beliefs at all. The evidence for paganism looks even weaker when archaeologists in England and mainland Europe are now revisiting the idea that 'furnished grave=pagan' (several tenth- and eleventh-century French bishops were buried in furnished graves!) and there are no securely dated furnished graves from Dublin from later than the beginning of the tenth century (as far as I'm aware anyway). Given Dublin's prominence in Irish Christianity in the eleventh-century (King Sitric, the same king who lost the ring of Thor and let the Thor's woods be burnt down, went on a pilgrimage to Rome in 1028 and founded Christ Church cathedral shortly afterwards; Dubliners and their bishop Dunán were the first and most enthusiastic adopters of the church reform movement in Ireland from the 1070s), I suspect that the various historical references to Thor, at least, are symbolic pagan hangovers in a city long Christianised.

TL;DR: Probably very similar to everywhere else in early medieval Ireland, as once Dublin gets big enough to be important after c.920, it was almost certainly totally Christianised, with only a few pagan/Thor-related hangovers which lasted to the year 1000.