Yes and no. Non-Catholics should not receive the Eucharist, but they can certainly participate in the rest of the service, joining in the prayers and songs and listening to the Bible readings.
SD
I'll add one additional qualification. Non-Catholics can participate in everything except actually receiving the Eucharist. You can even go up to the altar rail with your arms crossed over your chest and receive a blessing from the priest (many folks who are afraid they have a mortal sin on their conscience and haven't made it to confession will do this too.)
But there is ONE exception to this general rule, which my husband and I took advantage of. You'll find it in Canon 844 of the Church. In an emergency, IF you believe in all the doctrines of the Catholic church (Transubstantiation and the supremacy of the Pope are the usual sticking points), IF you ask permission ahead of time and of your own volition, and IF no minister of your own denomination is available, you MAY receive.
We did this when we were orphaned Episcopalians, after the awful General Convention when the homosexual adulterous "bishop" was "consecrated". We could no longer remain in communion with a heretical denomination, and since we were nosebleed-high Anglicans anyhow, there were absolutely no points of doctrinal difference (other than the validity of Anglican orders!) But we called on the Rector and talked it over with him first, and it was absolutely his call. (His opinion was that the ECUSA "bishop" was a walking emergency, all by himself.) < g >