You are confusing two different issues.
Permitting one Nation State (eg UK, Denmark or China) to have more than international football team is not the same as requiring/permitting two independent Nation states (eg UK and ROI) to combine two international football teams to create one.
As regards the former, there is no doubt that certain Associations within FIFA resent that the UK has four teams (though I would guess that this resentment may be less marked currently than during the 1980's and 90's i.e. when Scot and NI were qualifying for the WC Finals, as well as England).
That said, in addition to the written guarantees which the 4 Home Nations secured in return for rescuing FIFA from bankruptcy after WWII, the politics (small "p") of football also ensure that we have strong backing in other quarters.
For with FIFA operating on a "One Member, One Vote" basis, the other Confederations frequently gang up on UEFA in votes at Congress etc, despite UEFA providing the overwhelming bulk of FIFA's revenues and also being the powerhouse of world football, at both club and country level.
Therefore UEFA is only too pleased to have an extra three Member votes at FIFA. This explains why, for instance, on a busy international football evening in March last year, of all the matches Michel Platini might have attended, he picked a NI friendly with Georgia(!) at Windsor. Ostensibly, this was to present David Healy with a UEFA Goalscoring Award, but I have no doubt the real reason was to allow Platini to "press the flesh" with the recently elected IFA President, Raymond Kennedy.
By the same token, therefore, with just 53 UEFA Members out of 208 in FIFA, UEFA would likely be reluctant to lose even one extra Association's vote by merging the IFA and FAI.
And as I argued earlier, FIFA would also likely be hostile to such a move, albeit for reasons of principle, rather than "politics".
Therefore, I feel an all-UK Team poses a (marginally) greater threat to the IFA's independence than an all-Ireland team, but I'm not losing any sleep over either, tbh.
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