Picked up some Mrs. Renfro’s and Frontera yesterday and had them on tacos last night. Both salsas were decidedly non-chunky, yet both still maintained some texture.
You’re welcome. 
Salpica Salsa and Mrs. Renfro’s would both fit your criteria.
You can buy Salpica at www.fronterafiesta.com
I have their Urban Cowgirl Mango Peach topping my lunch today. Their products don’t have any preservatives so you have to consume it in the same time frame you would consume fresh salsa after you open the jar.
We discovered a ‘hole in the wall’ Mexican restaurant today. (Note: This does not mean it’s anywhere near the HITW restaurants in L.A.) They had different salsas on different tables, and ours had Yucatan Sunshine. I doused the chips with it, and it’s good.
Answer to the question you didn’t ask: homemade salsa is insanely easy. There isn’t one storebought product that this Texas woman can tolerate. There’s a goopy, slimy quality to most commercial salsas that I don’t like. (But, as commercial brands go, Herdez is a good product IMHO.)
Get two or three tennis ball-size tomatoes and one or two fresh, raw serranochiles (they’re the slender ones that are about the size and shape of a baby’s finger. Do NOT substitute a baby’s finger in this recipe).
Put all items in a pan with a rim (some juices may escape from the tomatoes), set in 400-ish degree oven until skins of tomatoes and peppers are charred. As very charred or slightly charred as appeals to you. You can also do this on a charcoal/gas grill.
Put everything in a blender with some salt. Keeps in the fridge or else (my preference) eat it all immediately with a ginormous bag of tortilla chips.
Variations abound… add lime, the dreaded and awful cilantro, onion, use jalapenos instead of serranos, and anything else that sounds good. Happily eat the experiments-- I mean, how bad can they be?
Also, you don’t have to put anything in the oven-- just blend it all raw.
I get my (non-chunky) salsa in the produce section at whatever grocery store I’m shopping at. Usually Walmart–their in-house (Market Fresh? Marketside? Market something…) salsa is really good; fresher than the bottled stuff, and just the right consistency.
It all seems so easy when you read it on a screen, but you clearly have never known what it’s like for me to be in a kitchen 
She left out the part about growing all the ingredients. 
She left out the onions.
My late-father gave me a Smart Chopper (As seen on TV!™) a couple of decades ago. I used to make salsa by throwing in a couple of tomatoes, a couple Serrano chiles, some onion, some cilantro, and a little salt and just chopping it all up. Of course it’s the opposite of not-chunky, but I like it.
Ahem. I wrote:
I read:
Onions were mentioned in variations!. Onions are not optional. 
Neither are cilantro and garlic!
it also needs some salt and a squeeze of lime juice.
Just a tip. You don’t have to make it yourself or get it in a grocery store. If you find a salsa you like in a restaurant, you can usually buy it in a tub from them.
For whatever reason standard grocery salsa is that chunky dogshit.
Go to any Mexican restaurant and you will NEVER see a chunk.
Opinions, opinions.
The basic salsa is tomatoes and peppers. The essential ingredients are tomatoes and peppers in order to call it salsa. Tomatoes and onions alone are not salsa. Onions and peppers alone are not salsa. You have to have tomatoes and peppers to start with. And yeah, add other stuff if you want to. I suggest you try it this way sometime just to see what it’s like without any other strong flavors coming into play.
Yes yes yes. Do this by all means.
Every time we plan a taco night, I stop by Cuca’s (a local taco joint) for 8 oz. of their house salsa. Great stuff, but it doesn’t store well. You have to get it the day you want to use it, or maybe the day before.