I am using Quarto 0.9.180 with Pandoc 2.5

Here is a sample qmd file

````markdown
---
title: "Test"
format: html
---

```{r}
data <- data.frame(X1 = c(1,2,3,4), 
                   X2 = c(5,6,7,8), 
                   X3 = c(9,10,11,12), 
                   Y = c('R', 'R','G', 'R'), 
                   stringsAsFactors = F)

colnames(data) <- c('$X_{1}$', '$X_{2}$', '$X_{3}$', '$Y$')

library(knitr)
library(kableExtra)

kable(data, row.names = TRUE) %>%
   kable_styling(bootstrap_options = "striped", full_width = F)

```
````
And here is the corresponding rmd file.

````markdown
---
title: "Test"
output: html_document
---

```{r}
data <- data.frame(X1 = c(1,2,3,4), 
                   X2 = c(5,6,7,8), 
                   X3 = c(9,10,11,12), 
                   Y = c('R', 'R','G', 'R'), 
                   stringsAsFactors = F)

colnames(data) <- c('$X_{1}$', '$X_{2}$', '$X_{3}$', '$Y$')

library(knitr)
library(kableExtra)

kable(data, row.names = TRUE) %>%
   kable_styling(bootstrap_options = "striped", full_width = F)
```
````

The two html outputs are [here](https://gist.github.com/meghanto/bd0083f9a41541f3633560692f28a6d3).
The quarto output does not render the math.

2022-04-06T20:57:12Z
meghanto
Future
open
Math formatting does not work in styled KableExtra tables
https://github.com/quarto-dev/quarto-cli/issues/555