A lot of jobs in Wales require you to be able to speak Welsh, especially in public service postions.
I've worked in the Welsh Language department of the Welsh Assembly, and I don't speak Welsh. Basicaly it is illegal for an employer to insist on the ability to speak a language unless the ability to speak that language is essential for the job - so I'd guess in a museum that could be because you'd be dealing with school trips, specific features on the welsh language, history etc. Otherwise the most they can do is move it into the "desirable" skills section, which many organisations just do to tick boxes anyway.
Call them, and ask for the justification. If they can't justify it being essential, then apply anyway.
Also WPMOT - I have head lice.