The anchovy paste (or anchovy fillets) really brings that umami flavor that is classic with traditional caesar salad. It’s a great thing and I definitely recommend it! But if you absolutely can’t do it, there are some substitutions you can make that will still keep it tasting like the real deal! Just omit the anchovy paste and sub for dijon mustard and Worcestershire sauce (about a tsp of each and then more to taste). You could also use fish sauce!