All the altcoins as a whole make up ~20% of the market cap of bitcoin (at least they did at the beginning of the year - I believe they have overall gone down in value since then so I am not sure where they stand now).
The peak was about 12%. The chart quoted below ends a couple of months ago at 4% and I'm pretty sure the number is lower now given the collapse of alt values (priced against BTC) over the past month.
The OP is completely wrong they are not hurting Bitcoin. If anything they are helping. Alt values against BTC are positively correlated with BTC values against USD. If alts were a substitute or threat you would expect a negative correlation, and that doesn't exist.
Interest in crypto whereever it comes from (for example, DOGE's much interest) helps all crypto. Lack of interest (for example the past month) hurts all crypto. But in reality the effect of alts is proportionate to their size which is tiny.