Ancestry has a baptism for Michael McBride on the date you have given. Parents were Arthur McBride and Mary McCaffry. Sponsors were James & Bridget McCaffry. The parents lived in the parish of Tempo which is close to Enniskillen in Co. Fermanagh. I can also see 2 siblings in those records, also baptised in Tempo:
I don’t see a marriage for Arthur and Mary. Tempo’s marriage records start in 1845. Perhaps they married there before that year, in which case there won’t be a record.
Death registration began in Ireland in 1864. I searched the death records for the death of an Arthur McBride 1864 – 1901 in the Enniskillen area. I only found 1. He died in Letterbailey on 16.9.1891 aged 73. A farmer and his wife was still alive. His son John was the informant. I also found the death of a Mary McBride in Letterbailey on 2.4.1897 aged 76. A widow, and her son John was the informant.
Probate abstract from the PRONI wills site:
Probate of the Will of Arthur M'Bride late of Letterbailey County Fermanagh Farmer who died 14 September 1891 granted at Armagh to Martin M'Quaid Farmer.
The will itself is on-line on the PRONI wills site and mentions his wife Mary, daughters Kate McBride and Bridget Owens and sons Hugh, Bernard & Mick. The farm was left to Kate.
This is John & his sister Catherine (ie Kate) in the 1901 census:
John died intestate in 1905:
Administration of the Estate of John McBride late of Letterbailey County Fermanagh Farmer who died 18 March 1905 granted at Armagh to Hugh McBride Farmer.
That all seems to fit your family.
Arthur McBride is listed in Griffiths Valuation for Letterbailey in 1862. He had plot 3 which was 13 and a half acres. A Francis McCaffrey senior was next door on plot 2. So I wouldn’t be surprised if Arthur had married the girl next door. Letterbailey today is on a minor road off the B80 road near Imeroo. It’s half a mile or so north of Campbell’s Quarry. 3 or 4 miles from Tempo village.
Bridget McBride married John Owens on 27.2.1870 in Tempo chapel. Both were from Letterbailey.
This is that couple in 1901:
John McBride (son of Arthur) married Margaret Owens on 23.2.1868 at Tempo chapel. After John’s death in 1905, this is Margaret and 2 children:
In the 1901 census John is with his sister Catherine on that farm, leaving his wife and son Bernard on their farm:
I can’t see Catherine (who was there in 1901) in the 1911 census. No death in the Enniskillen area nor a marriage. So possibly she had left Ireland. Presumably after her brother’s death keeping the farm going on her own was too much for her. According to the Valuation Revision records on the PRONI website, the farm remains in her name until 1914 when it changes to Bernard McBride. (So she might have died around that year). He was still tenant in 1929 when that series of records finishes. After his death in 1905, John McBride’s farm changed to Margaret then to Bernard and in 1918 to Hugh. He was still tenant in 1929.
I don’t see a marriage for Michael McBride to Anna Lynch in Ireland, so suspect they married elsewhere. If you search the US censuses or naturalisation papers it often tells you when they arrived in the US. Obviously if they arrived in different years that tends to point to them meeting in the US.