I notice from some of your earlier posts that you're in the East Midlands, which means you're covered by the Equality Act 2010, which makes it unlawful to discriminate against you on several grounds including gender identity. Hurrah!

But wait...
The law may well make it unlawful to discriminate against you, but how do you
prove that someone has done so?
Businesses can and do discriminate against applicants on
any grounds. They might not want women applying; or people with foreign-sounding names; or people above a certain age. Of course, it's illegal to discriminate on any of those grounds, but it's almost impossible to prove that that is the reason why you were rejected. Most employers who discriminate in such a manner will simply ignore that applicant's CV (or reject them at the interview stage) and if they're challenged on it, they'll just say that the vacancy has already been filled, or a more experienced candidate got the job, or they hired someone whose personality was a better fit for the team.
If you state you're trans at the early stages of the recruitment process, many employers will simply chuck your CV straight into the bin because they 'don't want the hassle'. I
guarantee it.
The smartest method I've come across is to not disclose your status during the application or interview process... but
do disclose it (to HR, in confidence) after you've received a job offer in writing. That way, you can use all the protections the law provides. You can take time off work for medical appointments to do with your transition (and no, you don't have to make that time up) and if any colleagues make transphobic comments, you can complain and they will have to be disciplined. And best of all, if the company suddenly withdraws their offer of employment after your disclosure, you have the evidence you need to nail them for it.
The one exception to the rule? If an employer is specifically looking to increase it's trans workforce, or if they work in the LGBT/trans sector, then disclosing your status at the application stage could be a huge asset.
It is the employer's responsibility to ensure you have a safe working environment free from harassment and discrimination, so if anything happens you must take it up with Management. You don't necessarily need to disclose your status, although it can strengthen your case if you do so when you complain. If you're stealth and someone says something offensive your first port of call might be to take them to one side and tell them you found it offensive (you don't need to explain why) and ask them to not say anything like that at work again. In many cases, that does the trick. But if they argue against you, or refuse to co-operate, or if the abuse gets worse, you must take it to your line manager and/or HR and keep going up the chain of command until the problem is fixed. Remember: dealing with troublesome co-workers - including the one who used religious harassment against you - is your
employer's responsibility, not yours.