Probably cedar apple rust

Here is a link that might be useful: Explanation, some pics

Oh dear. That's not good news. Once it is infected it will remain infected. Hate to say it but you may need to get rid of the tree outright.

Ianna

Don't know what is is but, I had the exact same "goop" on one grouping of cedars I have.....I had it once many years ago and it never came back.
I looked at your photos and the only difference is that my shrubs weren't covered as heavily as yours are...mine maybe 1/4 of your condition.
I just used my garden hose on heavy spray to remove the brown gelatinous stuff and rubbed and sprayed, and rubbed and sprayed. There was a buildup of fallen needles(is that what you call cedar foliage?) that got flushed out of the inner branches at the same time. It came off and never returned....I also thinned out the shrubs to allow more air/light to circulate.
Good luck to you, Justine

Oh yeah, at the time I thought they were some kind of insect eggs...
great gardening to you, Justine