the entrepreneur decides to give 20% of the business to person X, for free, as they feel person X can add tremendous value to the business
Yes that would dilute your percentage but not necessarily your value. Note that this seems to be an extraordinary example as the more typical example would be to sell the shares for their current value. In that case, your value would stay the same since you would own a smaller portion of a larger pie.
If instead that used shares as an incentive to employ someone else, then (assuming there's not fraud or stupidity involved) presumably that person would add an equivalent amount of value to the company, which would benefit you as well. So it's the same principle. If the present value of X's contributions was worth the same as the shares they're given, then you would still own a smaller portion of a larger pie (i.e. you would own a portion of the future benefits that person X brings). Now, if that person underperforms, that's bad for you as a shareholder, but it would be bad for you if they instead raised cash and used that cash unwisely.
That's much harder to quantify than a direct cash sale, but the principle is the same.
Can an entrepreneur issue new shares for the company and dilute me like this?
That's more of a legal question and it depends on the by-laws of the company and the laws in their jurisdiction, but it's not unusual for companies to issue more shares provided that have the approval of the board of directors and the existing shareholders, based on the by-laws of the company. Such issues can be dilutive but not always. Certainly fraud can happen which makes it important that you fully understand whatever you're investing in.