Pulse first 4 ingredients in a food processor until smooth.
Add thyme and next 2 ingredients; process until finely chopped.
Spread 1 Tbsp. cream cheese mixture onto each bread slice. Top with candy-cane beets and chives, or sliced squash and salmon caviar, pressing lightly. Trim crusts from bread.
Cut each bread slice into 4 squares or 2 rectangles.