Thanks to @Andy Baxter in the comments. Here is an effective workaround.

> perf3 <- perf2 %>% 
+   select(first.half, second.half, t.reg.date2) %>% 
+   mutate(t.reg.date3=parse_date_time(paste0(first.half, second.half), "%Y-%m-%d", exact = TRUE)) 
Warning message:
There was 1 warning in `mutate()`.
ℹ In argument: `t.reg.date3 = parse_date_time(...)`.
Caused by warning:
!  43047 failed to parse.