That is clearly not true.
Try working in the public sector and claiming that you believe that marriage is between male and female. Take a trip over to the Christian Institute website when you have time and you will see a whole host of cases where Christians have been discriminated against, simply because of what they believe.
Do not try and weasel your way out of this by claiming that it is because of their actions, not their beliefs. That only makes your position worse as it implies there is a morality that comes with secularism, that must be enforced.
I've looked at the Christian Institute website from your link, and they appear to be a bunch of right-wing, narrow-minded, curtain-twitching busy-bodies. You talk of "Christians being discriminated against because of what they believe", but when what they believe is itself discriminatory, the more their beliefs are accommodated, the more others are discriminated. We saw that in the C of E, with the "Backward in Bigotry" misogynists demanding ever more outrageous concessions to their prejudice, and the more churches where women are not allowed as vicars, the less equal women priests are. The same applies to gays, etc. Incidentally, the Christian Institute certainly doesn't speak for all, or even, I suspect, a majority, of Christians - it emphatically doesn't speak for me. Right-wing evangelicals do have the very bad habit of referring to themselves as "Christians" without qualification, as though their joyless (per)version of the faith represents all of Christianity.