I am wondering if anyone could give me advice on the arborvitae. They are growing great but I am concerned that the privacy row is getting too tight. Should I remove every other plant to give them more room for growth?
In my opinion, you should not remove every other plant - keep them all.
The problem is: thujas generally don't grow from "old wood". If you remove every other thuja, you will probably find areas at neighboring thujas that do not have green leaves. From these areas, there will be no new growth - only the growth from surrounding, green-leaved areas may fill in the space. But this would be a really long process - five to ten years.
Some kinds of thuja (let's say, thuja plicata) may grow from old wood - still very depending on the microclimate (sun exposure, etc.). But I think your thujas are thuja occidentalis, that is not growing from old wood, except some rare cultivars.
In time, all thujas in your screen will merge, and you can, without negative effects on the plants, gently trim the sides and/or tops in accordance to your taste. Watch that you do not reach "dead", brown, zone while you trim them.
Thujas will naturally tolerate neighboring ones, that is exactly why they are used for screens like yours.
Some additional info: I see some (majority?) of your thujas have multiple leaders. there is nothing wrong biologically about that, however, it may represent a problem if you have heavy snow - snow may bend some branches and they could permanently be left in such ugly position - the solution is to keep a careful eye on your thujas during snowy winters. Another solution is to cut completely all but a single leader now, but the downside is that this again may leave some brown inner areas visible.
I think your screen is beautiful, and you could keep it, basically, as is.