A: Only if your parents or other relatives object to your transition so strenuously that they exclude you from their wills.
There are two basic types of inheritance in the United States, testate and intestate succession. Testate refers to the situation in which the deceased person prepared a will describing how they want their property distributed.
A typical will for a married person will leave everything to the spouse, and then to the children if the spouse does not happen to survive the testator (the person making the will), possibility with a few specific bequests (particular items designated to go to particular people). So long as the testator was competent at the time the will was made, and was not coerced, the provisions of the will shall be enforced by the courts. Competent, for the purposes of a will, means that the person knows who her relatives are (the natural objects of her bounty), and the extent of her assets.
Enforcement of the provisions of a will can mean denying an inheritance to a child who was excluded from the will, either by intentional omission or specifically disinherited. This is a possibility if your parents are sufficiently upset. On a more positive note, most people don't change their wills when they really need to, so even an upset parent may not get around to it - or may say they will do it but not mean it. The will controls, no matter what the testator may say at a later time.
The other vehicle is intestate succession. This is the situation where a person dies without a will. In this case, the statutes dealing with probate matters in your state will determine how a decedent's estate is distributed. In California, for example, that is governed by Probate Code Sections 6400 - 6414, and these statutes divide an intestate estate. How it is divided depends on whether there is a survivivng spouse, surviving children, surviving parents, issue of deceased children, etc. In other words, it can get a bit complicated, but will be controlled by a state statute.
Whether you would inherit under a will or by intestate succession, will not be affected by your transition (absent being disinherited). If you inherit by will, the executor (the person who is in charge of distributing the estate) likely knows who you are, and would list you among the heirs. Otherwise, claiming your share of the estate is really only a matter of proving who you are and were - that Simone Smythe used to be Seymour Smith - and with name changes being common in our society, this really isn't much of a problem.