Does immunity to CRISPR proteins limit their effectiveness?

Usually not. the Crispr/Cas proteins can be delivered to the cell as DNA/RNA and the proteins will only exist inside the cell in low numbers.

Even in systems that deliver the protein from the outside in vivo almost always the proteins would be encapsulated in a delivery system to ensure they and any necessary accompanying nucleic acids get into the cell. Getting Crispr/Cas into a cell is difficult to do and they don't just pop in by themselves. They also require guide RNA, which will not easily stay whole in the blood stream and tissues for long.

if you want to just inject a fluid into the blood with unprotected CRISPR/CAS proteins, an immune reaction might stop them. Not all proteins produce an immune reaction. Sometimes just 2-3 proteins of an entire bacterium produce an immune reaction (antibodies). But then again its unlikely the proteins would have edited any genomes in any host cells even so.