I can't reproduce your issue, the code you have provided runs as expected on my setup (R 4.2.0 on Ubuntu Server 20.04 LTS, dplyr 1.0.9), see this reprex.
library(dplyr)
iris_test1 <- iris %>%
group_by(Species) %>%
summarise(Petal.Length_mean_value = mean(Petal.Length))
iris_test2 <- iris %>%
group_by(Species) %>%
summarise(Petal.Width_mean_value = mean(Petal.Width))
iris_test1 %>%
dplyr::full_join(iris_test2, by = 'Species')
#> # A tibble: 3 × 3
#> Species Petal.Length_mean_value Petal.Width_mean_value
#> <fct> <dbl> <dbl>
#> 1 setosa 1.46 0.246
#> 2 versicolor 4.26 1.33
#> 3 virginica 5.55 2.03
Created on 2022-05-12 by the reprex package (v2.0.1)
As Nir says, maybe the full_join() function is being masked by another package, to test this theory you can run the code this way:
iris_test1 %>%
dplyr::full_join(iris_test2, by = 'Species')