Yes, the new law could easily be used to restrict speech, it includes the new offence of "stirring up hatred," which is an incredibly broad and undefined term to use.
The Scottish Police Federation said the bill would result in officers "policing what people think or feel"
The only Nazis I'm aware of in Scotland are the members of the SNP, luckily I'm not in Scotland or saying this would probably count as a hate crime under the new bill.