The only real solutions here are:

Set the backup app to snapshot the machine but exclude the databases. Some tools can, some can't. If you have a good SQL backup strategy, as it sounds like you have, then there isn't a need to snapshot the databases as well.

Set the backup app to do a 'copy only' snapshot. Probably won't be an option, haven't seen that as a setting in many tools.

Change the backup strategy to be a mix of full and log backups. If you're not doing differentials then the additional full backups won't have any effect on restoring. Not the best option, probably the last option if nothing else is possible

As soon as a full backup is taken without the copy only option, it becomes the differential base for the next full backups, regardless of how that full backup was taken. The full backup however has no effect on log backups, regardless of options or how they were taken.