TLDR: The mood of were in “If I were you” is either irrealis or subjunctive (past tense), depending on which grammarians you listen to.
There is a battle over terminology currently going on among grammarians. Some grammarians refer to the verb in “If I were you” as the past subjunctive (See for example, this Grammar girl post), labeling it as past tense and subjunctive mood. Others refer to it as the irrealis mood (See for example the footnote here). Wikipedia for now seems to have decided to go with the irrealis label. For example, in the Wikipedia article on the English subjunctive, the terminology past subjunctive for irrealis seems to be classified as a “misconception”, rather than as a possibly superseded name, which would be more accurate.
There are advantages and disadvantages of this change in terminology. An advantage is that in contemporary English, the past subjunctive, or irrealis, has very little grammatical relation to the present subjunctive, also known as the mandative subjunctive.
A disadvantage is that, historically, both the mandative subjunctive and the irrealis are derived from a subjunctive mood that was used much more broadly; you can visualize these as being two small islands that are left of a much larger subjunctive landmass that has been inundated by the rising waters of the indicative.
Another disadvantage is that trying to change terminology inevitably ends up confusing people, even if you have good reasons for changing it. My personal opinion is that the change is too recent for people to be calling one or the other label “wrong”.