I'm not well-versed in OT times or anything, but ISTM the celebration in the psalm is not in any way liturgical or connected with their actual worship. It's praise. Catholics can play tambourines and dance and praise God, just not as a part of Mass. (Though even outside of Mass they should take care that this form of praising God is not about entertainment and isn't too emotionally-driven and isn't undignified or immodest and so forth.)
OK, that was basically where I went with my response. I asked, "Dance and joy yes, but did they do that in the temple?"
Which neither of us knew the answer to.
I think "God centered" and "modesty" are key words.