Do the phage repressors CI and Mnt exhibit crosstalk?
There are no reports for it yet. I don't think just because they show overall homology, they would exhibit crosstalk. Just see the alignment of the DNA binding domains of these proteins first ~70 residues from N-terminal. Moreover their DBDs belong to different PFAM families.

Similarly with the promoter sequences.
As reported in iGEM website:


Mnt promoter: tagatctcctatagtgagtcgtattaattt
cI promoter: gtgttgactattttacctctggcggtgata    


They are quite different.
Moreover, if iGEM has a reported standard part such as a bistable system component: Mnt/cI promoter (BBa_K228003) then it would have been pretty much standardized. iGEM parts are usually reliable.