Having FIPS mode enabled causes the .NET Framework to disallow the use of non-validated algorithms and this can cause problems installing and upgrading Redgate tools.
This issue can be resolved by turning FIPS compliance off. This can be done in the Local Security Policy (however if you are in a Domain this might be overridden by Group Policies, so you might need to speak to your Windows System Administrator).
Microsoft no longer recommend FIPS mode as detailed here.
If turning FIPS off is not an option you should be able to workaround this by editing the xml file:
C:\Program Files (x86)\Common Files\Red Gate\Shared Client\RedGate.Client.Service.exe.config
and adding the following under