Subsetting two binary variables?

I'm not sure how this is possible. Indeed, the approach you use should work, as can be made clear with an example:

df <- data.frame(id=1:10,
                 POPULIST = c(rep(1,4), rep(0,6)),
                 EUROSCEPTIC = c(rep(0,2),rep(1,4), rep(0,4)))


df
#>    id POPULIST EUROSCEPTIC
#> 1   1        1           0
#> 2   2        1           0
#> 3   3        1           1
#> 4   4        1           1
#> 5   5        0           1
#> 6   6        0           1
#> 7   7        0           0
#> 8   8        0           0
#> 9   9        0           0
#> 10 10        0           0
subset(df, POPULIST == 1 | EUROSCEPTIC == 1)
#>   id POPULIST EUROSCEPTIC
#> 1  1        1           0
#> 2  2        1           0
#> 3  3        1           1
#> 4  4        1           1
#> 5  5        0           1
#> 6  6        0           1

Created on 2020-12-06 by the reprex package (v0.3.0)

So to understand what's wrong in your case, it could help if you made a minimal reproducible example, see some guidelines here:

PS: to get a better look at your data and see what number of parties to expect, you could try to tabulate POPULIST vs EUROSCEPTIC like that:

table(df$POPULIST, df$EUROSCEPTIC)
#>   
#>    0 1
#>  0 4 2
#>  1 2 2