Dean,
The RIC is not my area of interest but this badge does not look like RIC to me.
This type of design looks far more like that used on undress caps of the London Irish ( 28th Middlesex Volunteer) Rifles such as the Kilmarnock and the Glengarry. I have seen styles with loops and screw posts as fitments. There are various stylistic differences such as in the number of the strings but the aspect ratio and that distinctive joint with the crown are all quite similar. But whether it actually is London Irish I cannot say for sure.
For a more definitive answer on possible RIC use I would advise you contact Peter at
https://irishconstabulary.com/
John