Is it possible for inflation to equally affect all people?
Short answer, no. Long answer, no because everyone can be affected by inflation but not everyone will be affected equally. Every family has a different level of income, expenses, different monetary habits and such. If a family is more affluent and wealthy, they will have less of a problem with inflation than a family that is in the lower class who will experience inflation to a greater effect. This is just my thoughts/answer, Professor Danny can add anything else if he wishes.
Jed is correct. If you do not have assets that inflate (imagine a poor family with no money in the stock market, no gold, not owning a home, etc.) then inflation only hurts the purchasing power of the dollars you have in savings or the dollars you earn each month before you get a raise to keep up with inflation. The wealthy, however, benefit greatly from inflation. If you are a CEO being paid in stock, the stock of any particular company will only increase with inflation. CEOs are a hedge case, but consider, say, a doctor. They are much more likely to have a high enough income to get by with higher prices, and their assets (stocks, gold, home, lake house, etc.) are all increasing in price due to inflation. It truly is a curious case why progressives support policies that lead to inflation when inflation is a very regressive outcome.