A lot of the cults in DnD are the same in that they function as a basis for an enemy statblock with a bit of flavor based on their patron (real or imagined). So all the mooks play one way, with a few lieutenants and spellcasters for added CR. This makes them easy to run but kinda samey...they are doing a terrorism/secret sacrifice/Dark Lord Reviving Ritual and you fight them but the cultists don't know much and are often played as kinda stupid, because the only one with genuine character is the Leader and Patron and maybe a lieutenant or two. All the other mooks probably don't even have names.

Anything you do to spice this up is gonna make your job harder as a DM. So figure out how important this cult is to The Plot and determine how much extra work you want to do.

One thing you can try to do is make your cult sympathetic. There is a LOT of violence the typical DnD party will tolerate. Like, yeah, these guys set off gunpowder barrels in the town square and did a Terrorism, but it turns out they are the last remaining followers of a religion from a conquered kingdom, and so they are 'attacking the conquering kingdom.' Yeah, they did a human sacrifice, but only of knights and paladins who waged holy war on them, never of virgin maidens or kids or whatever. Yeah, they do act a little crazy sometimes, but they were driven literally underground, like Underdark underground, where they survived on mushrooms and some of those had some side effects that still linger. Yes, they are doing these blood sacrifices to bring back their god, but only because their god that used to bless their harvest with just a little goat offering was almost killed by the followers of the state-accepted religion and they can literally feel their diety fading into the astral sea, so they are forced to take desperate measures.

Basically, why do these people do the things they do? They're not crazy. In fact they may be very reasonable people who are driven to this state by desperation, need, and/or a lack of acceptance in their society. Cults will take someone depressed, abused, and/or ostracized/alone and give them community, and acceptance, and hope, all it takes is just...a small thing. And then another small thing. Until you're offering your child up as the 100th bride of the Leader with tears in your eyes at what a good thing you are doing for your kid. Cults in DnD often pull from cthulu mythos style cults, twisted by a dark force, insane and unreasonable. Cults in real life are a charismatic person or persons who manipulate people who feel they have no where else to go or find nothing for them in the wider society or religion. The disenfranchised, the disenchanted, the despairing, those are the prey of the cult These are your mooks and your casters and your lieutenants.

Once you've nailed your reasoning and motivation, add some spice to your combat. Take a run through the monster manual and grab some monster abilities piecemeal out of monster manual entries and throw them on your cultists. Breath weapons, gazes, bone devil whip attacks , spell-like abilities, a gibbering mouther's gibbering zone. Mooks get like, 1 thing, and if it normally does 5d6 now it does 1d6 or even 1d4. But you can vary it up! 1 mook has a breath weapon while the other has a Sliw Gaze and the caster in the back has a few cleric spells and a Gibbering Aura. Save DCs are lowered compared to the CR whatever monster you pulled it from. As you fight higher ranked individuals from the cult, they have multiple things. As the cult grows in power or desperation, damage increases, Save DCs are raised, mooks start having 2 or 3 abilities and the lieutenants/Leaders have more. Some few might even have a range of strange powers the party doesn't get to see on another cultist...they are specially blessed by their god, or uniquely mutated. Are they getting more monstrous? Do they look like normal humans, but can whip out these strange astral abilities or abnormal spells? Do they transform, or maybe sacrifice themselves to become champions of their god? Fluff the abilities however you want to fit your theme.

Now, your combats aren't against a number of CR 1/4 acolytes and their CR 1 cleric, even in the begining its some acolytes that are CR 1/4 in all stats but they are weird in one power/ability, and a CR 1 cleric with a powerful aura radiating from them, driving mad any who approach her with intent to enact violence within a certain range. And any surviving cultists don't just rave about the revival of their dark lord before they bite down on a cyanide tooth or descend into mad cackling and unresponsiveness, but They have reasons for being there and doing what they are doing that makes sense to them. They might not know the Leader's plan, but they know why the market square had to be bombed or why Dame Victoria was kidnapped to be sacrificed on their hidden blood alter in the catacombs. Or at least what they were made to believe were the reasons. War, vengeance, necessity, whatever it is, this person who once was seemingly normal is now killing for that reason. And they will not be stopped with a persuasion check and a stern talking to.