I know plenty pf BTs and gerim who don’t let their past define them, and havd totally embraced yiddishkeit in every possible way. They are true bnei torah and don’t deviate from their yeshiva or chasidus an inch. And no one has a problem with them.
The only difference is in rebbehe shiduchim, where they won’t get rehdt to a rebbishe einikel…nu nu.
But in Litvishe yeshivos, BTs have married roshei yeshiva; it’s more of a meritocracy.
And in Lubavitch their pool of shiduchim is even more limited.