I've been told that RAM hasn't been offered to Taiwan. It's a US-German project - does that mean the Germans can veto a sale? If so it's unlikely they'll allow it being offered to Taiwan anytime soon.
Technically RAM is a self-defense weapon, so there should be less opposition to its export. However if it's ever sold to ROCN, I suspect it'd be the less capable variant (Sea RAM?) at inflated prices.
The issue here is that the ROCN is expected to act as a shield and sink any PLAN ships that comes through the Taiwan Strait, which is approx. 130km-180km. At the rate that AShM's are increasing in its effective distance, I expect the PLA/PLAN to be able to shoot at ROCN ships without leaving their own coastal bases.
The number of missiles that a ship can carry is very limited by space and weight restrictions, versus land-based systems have virtually unlimited space/weight. So in an extended battle of attrition, the ROCN ships are at an absolute disadvantage. Fitting ancient SM-1 box launchers, or installing new RAM systems would only be useful for self-defense in skirmishes, or one-time incidents.
On the flip side, the same advantage can be enjoyed by the ROCA/ROCN, should they field many land-based mobile AShM systems, along with an effective air force and air defense system to protect them. Most strike aircraft can only carry 2-4 anti-ship missiles, but if the enemy is confined to an area no more than 180km wide, you could always send the target data back to base and have ground-based missile battery send a salvo of anti-ship missiles over. As the defending side, the ROCA/ROCN only needs to sink PLAN transports to "win".