Civil marriage registers certainly confirm that when Thomas Crawford married Agnes Crawford on 22 February 1882 in Raloo Presbyterian Church, his father was recorded as Thomas Crawford (scanned image of this marriage entry can be viewed at https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1882/10955/8004284.pdf ).
Prior to 1864 and civil registration of births in Ireland you will have to rely on church registers to confirm birth details of Thomas Crawford (born 1852) and of his parents, grandparents etc. Dates of commencement and quality of information in church registers vary from parish to parish and from denomination to denomination. Access to church registers, in the absence of indexes and databases, is generally gained through knowledge of an ancestor's parish address and religious denomination.
There is no national index to Irish church registers. To date, only the county-based genealogy centres have attempted any large scale, systematic indexing of church registers in their localities. Although RootsIreland, www.rootsireland.ie , is the largest online source of Irish church register transcripts, it must be emphasised that a failure to find relevant birth/marriage entries in this database doesn't mean that the events you are looking for didn't happen in Ireland. It simply means that they are not recorded in the database; for example, they may be recorded in a record source which doesn't survive for the time period of interest or in a source that has not been computerised. You can view details of all County Antrim church registers, with dates, that are available to search on RootsIreland at https://rootsireland.ie/antrim/online-sources.php.
If you wish to identify all available church registers in the wider Braid/Broughshane/Raloo area of County Antrim, microfilm copies of which are held in our national archives in the Public Record Office of Northern Ireland (PRONI) in Belfast you should explore their Guide To Church Records, which can be accessed on their website at https://www.nidirect.gov.uk/publications/proni-guide-church-records as it lists, in alphabetical order by civil parish, church registers of all denominations for most parishes in Ulster and their commencement dates, together with their microfilm reference details
Information provided by Brian / Tower Museum