First, let it be clear that I think it is silly for us to have to change language in order to appease the squeaky wheel.
I think that if someone says, "If any man would follow me, let him take up his cross and follow me," everyone knows that he is talking generically. There is no need to say, "If any person would follow me, let him OR HER take up his OR HER cross and follow me."
However, let me point out that those who claim that gender-neutral translations are inaccurate do so on weak grounds. The complaint is that gender-neutral translations change the wording of the Bible. This simply isn't true.
Here is the crucial question: if the Greek uses a masculine pronoun, does it always mean male only, or can it include both genders? The answer to this is, of course, that it can include both genders.
This being the case, then the question arises, Which pronoun in English is best to use in order to convey the inclusion of both genders?
My answer, as indicated in the first couple of paragraphs above, is that the masculine gender is perfectly capable of conveying the inclusion of both genders. However, if an English translation does indeed use some means of conveying the inclusion of both genders, it does not follow that the genderless translation is inaccurate.
If the genderless translation reads, "If any person would follow me, let him OR HER take up his OR HER cross and follow me," it may be cumbersome and pedantic, but it is nonetheless accurate. The same is true for, "If anyone would follow me, let them take up their cross and follow me."
If we want to criticise NLT, NRSV, TNIV, etc., for something, let us criticise them for being so committed to appealing to the spirit of the day as to produce awkward translations. But we cannot criticise them for producing inaccurate translations.
And let us not forget that even the ESV, which in its sales propaganda criticises these other versions for their gender neutrality, consistently translates the Hebrew phrase for "the sons of Israel" as "the children of Israel"--which boggles my mind given the ESV translation philosophy.